Package 'ahead' reference manual

Title:	Time Series Forecasting with uncertainty quantification
Description:	Univariate and multivariate time series forecasting with uncertainty quantification.
Authors:	T. Moudiki
Maintainer:	T. Moudiki <[email protected]>
License:	BSD_3_clause Clear + file LICENSE
Version:	0.13.0
Built:	2024-09-16 16:22:24 UTC
Source:	https://github.com/Techtonique/ahead

ARMA(1, 1)-GARCH(1, 1) forecasting (with simulation)

Description

ARMA(1, 1)-GARCH(1, 1) forecasting (with simulation)

Usage

armagarchf(
  y,
  h = 5,
  level = 95,
  B = 250,
  cl = 1L,
  dist = c("student", "gaussian"),
  seed = 123
)
armagarchf(
  y,
  h = 5,
  level = 95,
  B = 250,
  cl = 1L,
  dist = c("student", "gaussian"),
  seed = 123
)

Arguments

`y`	a univariate time series
`h`	number of periods for forecasting
`level`	confidence level for prediction intervals
`B`	number of simulations for 'arima.sim'
`cl`	an integer; the number of clusters for parallel execution
`dist`	distribution of innovations ("student" or "gaussian")
`seed`	reproducibility seed

Value

An object of class "forecast"; a list containing the following elements:

`model`	A list containing information about the fitted model
`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`x`	The original time series
`sims`	Simulations of ARMA(1, 1)-GARCH(1, 1)

Author(s)

T. Moudiki

Examples


y <- datasets::EuStockMarkets[ , "DAX"]
log_returns <- ts(log(y[-1]/y[-length(y)]))

# require(forecast)
# z <- ahead::armagarchf(y=log_returns, h=200)
# plot(z)


y <- datasets::EuStockMarkets[ , "DAX"]
log_returns <- ts(log(y[-1]/y[-length(y)]))

# require(forecast)
# z <- ahead::armagarchf(y=log_returns, h=200)
# plot(z)

Basic forecasting (mean, median, random walk)

Description

Basic forecasting functions for multivariate time series

Usage

basicf(
  y,
  h = 5,
  level = 95,
  method = c("mean", "median", "rw"),
  type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap"),
  block_length = NULL,
  seed = 1,
  B = 100,
  show_progress = TRUE
)
basicf(
  y,
  h = 5,
  level = 95,
  method = c("mean", "median", "rw"),
  type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap"),
  block_length = NULL,
  seed = 1,
  B = 100,
  show_progress = TRUE
)

Arguments

`y`	A multivariate time series of class `ts` or a matrix
`h`	Forecasting horizon
`level`	Confidence level for prediction intervals
`method`	forecasting method, either "mean", "median", or random walk ("rw")
`type_pi`	type of prediction interval currently, "gaussian", "bootstrap", "blockbootstrap" or "movingblockbootstrap"
`block_length`	length of block for (circular) "blockbootstrap" or "movingblockbootstrap"
`seed`	reproducibility seed for `type_pi == 'bootstrap'`
`B`	Number of bootstrap replications for `type_pi == 'bootstrap'`
`show_progress`	A boolean; show progress bar for bootstrapping? Default is TRUE.

Value

An object of class "mtsforecast"; a list containing the following elements:

`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`sims`	Model simulations for bootstrapping (basic, or block)
`x`	The original time series
`residuals`	Residuals from the fitted model
`coefficients`	Regression coefficients for `type_pi == 'gaussian'` for now

Examples


require(fpp)

res <- ahead::basicf(fpp::insurance, h=10)
par(mfrow=c(1, 2))
plot(res, "TV.advert")
plot(res, "Quotes")


res <- ahead::basicf(fpp::insurance, method="rw", h=10)
par(mfrow=c(1, 2))
plot(res, "TV.advert")
plot(res, "Quotes")


# block bootstrap
res3 <- ahead::basicf(fpp::insurance, h=10, type_pi = "bootstrap", B=10)
res5 <- ahead::basicf(fpp::insurance, h=10, type_pi = "blockbootstrap", B=10,
                      block_length = 4)

print(res3$sims[[2]])
print(res5$sims[[2]])

par(mfrow=c(2, 2))
plot(res3, "Quotes")
plot(res3, "TV.advert")
plot(res5, "Quotes")
plot(res5, "TV.advert")


# moving block bootstrap
res6 <- ahead::basicf(fpp::insurance, h=10,
                      type_pi = "movingblockbootstrap", B=10,
                      block_length = 4, method = "rw")

par(mfrow=c(1, 2))
plot(res6, "Quotes")
plot(res6, "TV.advert")

require(fpp)

res <- ahead::basicf(fpp::insurance, h=10)
par(mfrow=c(1, 2))
plot(res, "TV.advert")
plot(res, "Quotes")


res <- ahead::basicf(fpp::insurance, method="rw", h=10)
par(mfrow=c(1, 2))
plot(res, "TV.advert")
plot(res, "Quotes")


# block bootstrap
res3 <- ahead::basicf(fpp::insurance, h=10, type_pi = "bootstrap", B=10)
res5 <- ahead::basicf(fpp::insurance, h=10, type_pi = "blockbootstrap", B=10,
                      block_length = 4)

print(res3$sims[[2]])
print(res5$sims[[2]])

par(mfrow=c(2, 2))
plot(res3, "Quotes")
plot(res3, "TV.advert")
plot(res5, "Quotes")
plot(res5, "TV.advert")


# moving block bootstrap
res6 <- ahead::basicf(fpp::insurance, h=10,
                      type_pi = "movingblockbootstrap", B=10,
                      block_length = 4, method = "rw")

par(mfrow=c(1, 2))
plot(res6, "Quotes")
plot(res6, "TV.advert")

Create trend and seasonality features for univariate time series

Description

Create trend and seasonality features for univariate time series

Usage

createtrendseason(y)
createtrendseason(y)

Arguments

`y`	a univariate time series

Value

a vector or matrix of features

Examples


y <- ts(rnorm(100), start = 1, frequency = 12)
createtrendseason(y)

createtrendseason(USAccDeaths)

y <- ts(rnorm(100), start = 1, frequency = 12)
createtrendseason(y)

createtrendseason(USAccDeaths)

Dynamic regression model

Description

Adapted from forecast::nnetar, with alternative fitting functions (see examples)

Usage

dynrmf(
  y,
  h = 5,
  level = 95,
  fit_func = ahead::ridge,
  predict_func = predict,
  fit_params = NULL,
  type_pi = c("gaussian", "E", "A", "T"),
  xreg_fit = NULL,
  xreg_predict = NULL,
  ...
)
dynrmf(
  y,
  h = 5,
  level = 95,
  fit_func = ahead::ridge,
  predict_func = predict,
  fit_params = NULL,
  type_pi = c("gaussian", "E", "A", "T"),
  xreg_fit = NULL,
  xreg_predict = NULL,
  ...
)

Arguments

`y`	A numeric vector or time series of class `ts`
`h`	Forecasting horizon
`level`	Confidence level for prediction intervals
`fit_func`	Fitting function (Statistical/ML model). Default is Ridge regression.
`predict_func`	Prediction function (Statistical/ML model)
`fit_params`	a list of additional parameters for the fitting function `fit_func` (see examples)
`type_pi`	Type of prediction interval (currently "gaussian", ETS: "E", Arima: "A" or Theta: "T")
`xreg_fit`	Optionally, a vector or matrix of external regressors, which must have the same number of rows as y. Must be numeric.
`xreg_predict`	Future values of external regressor variables.
`...`	additional parameters

Value

a list; an object of class forecast.

The function summary is used to obtain and print a summary of the results.

The generic accessor functions fitted.values and residuals extract useful features.

Author(s)

T. Moudiki

References

Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts.

Hyndman R, Athanasopoulos G, Bergmeir C, Caceres G, Chhay L, O'Hara-Wild M, Petropoulos F, Razbash S, Wang E, Yasmeen F (2021). forecast: Forecasting functions for time series and linear models. R package version 8.14, <URL: https://pkg.robjhyndman.com/forecast/>.

Examples


# Example 0: with Ridge regression

par(mfrow=c(3, 2))
plot(dynrmf(USAccDeaths, h=20, level=95))
plot(dynrmf(AirPassengers, h=20, level=95))
plot(dynrmf(lynx, h=20, level=95))
plot(dynrmf(WWWusage, h=20, level=95))
plot(dynrmf(Nile, h=20, level=95))
plot(dynrmf(fdeaths, h=20, level=95))


# Example 1: with Random Forest

## Not run: 

require(randomForest)

par(mfrow=c(3, 2))
plot(dynrmf(USAccDeaths, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(AirPassengers, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(lynx, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(WWWusage, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(Nile, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))

## End(Not run)

# Example 2: with SVM

## Not run: 

require(e1071)

par(mfrow=c(2, 2))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "linear"), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "polynomial"), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "radial"), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "sigmoid"), predict_func = predict))


## End(Not run)


# Example 0: with Ridge regression

par(mfrow=c(3, 2))
plot(dynrmf(USAccDeaths, h=20, level=95))
plot(dynrmf(AirPassengers, h=20, level=95))
plot(dynrmf(lynx, h=20, level=95))
plot(dynrmf(WWWusage, h=20, level=95))
plot(dynrmf(Nile, h=20, level=95))
plot(dynrmf(fdeaths, h=20, level=95))


# Example 1: with Random Forest

## Not run: 

require(randomForest)

par(mfrow=c(3, 2))
plot(dynrmf(USAccDeaths, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(AirPassengers, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(lynx, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(WWWusage, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(Nile, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = randomForest::randomForest,
     fit_params = list(ntree = 50), predict_func = predict))

## End(Not run)

# Example 2: with SVM

## Not run: 

require(e1071)

par(mfrow=c(2, 2))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "linear"), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "polynomial"), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "radial"), predict_func = predict))
plot(dynrmf(fdeaths, h=20, level=95, fit_func = e1071::svm,
fit_params = list(kernel = "sigmoid"), predict_func = predict))


## End(Not run)

Combined ets-arima-theta forecasts

Description

Combined ets, arima, and theta (eat) forecasting (uses forecast::ets, forecast::auto.arima, forecast::thetaf)

Usage

eatf(
  y,
  h = 5,
  level = 95,
  method = c("EAT", "E", "A", "T"),
  weights = rep(1/3, 3),
  type_pi = c("gaussian", "E", "A", "T"),
  ...
)
eatf(
  y,
  h = 5,
  level = 95,
  method = c("EAT", "E", "A", "T"),
  weights = rep(1/3, 3),
  type_pi = c("gaussian", "E", "A", "T"),
  ...
)

Arguments

`y`	a univariate time series
`h`	number of periods for forecasting
`level`	confidence level for prediction intervals
`method`	forecasting method: "E" for `forecast::ets`; "A"for `forecast::auto.arima`; "T" for `forecast::thetaf`; or "EAT" for the combination of the three (default, with `weights`)
`weights`	weights for each method, in method `EAT`. Must add up to 1.
`type_pi`	type of prediction interval: currently ETS: "E", Auto.Arima: "A" or Theta: "T"
`...`	additional parameters to be passed to `forecast::ets`, `forecast::auto.arima`, `forecast::thetaf` and `forecast::forecast`

Details

ensemble forecasts obtained from forecast::ets, forecast::auto.arima and forecast::theta (with weights)

Value

An object of class "forecast"; a list containing the following elements:

`model`	A list containing information about the fitted model
`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`x`	The original time series
`residuals`	Residuals from the fitted model

Author(s)

T. Moudiki

References

Hyndman RJ, Khandakar Y (2008). 'Automatic time series forecasting: the forecast package for R.' Journal of Statistical Software, 26 (3), 1-22. <URL: https://www.jstatsoft.org/article/view/v027i03>.

Assimakopoulos, V. and Nikolopoulos, K. (2000). The theta model: a decomposition approach to forecasting. International Journal of Forecasting 16, 521-530.

Hyndman, R.J., and Billah, B. (2003) Unmasking the Theta method. International J. Forecasting, 19, 287-290.

Examples


require(forecast)

## Not run: 

print(ahead::eatf(WWWusage, method = "EAT",
weights = c(0.5, 0, 0.5)))

print(ahead::eatf(WWWusage, method = "EAT"))


obj <- ahead::eatf(WWWusage, method = "EAT",
weights = c(0, 0.5, 0.5), h=10,
type_pi = "T")
plot(obj)


obj <- ahead::eatf(WWWusage, method = "EAT",
weights = c(0, 0.5, 0.5), h=10, type_pi="A")
plot(obj)

## End(Not run)


par(mfrow=c(3, 2))
plot(ahead::eatf(USAccDeaths, h=10, level=95))
plot(ahead::eatf(AirPassengers, h=10, level=95, type_pi = "T"))
plot(ahead::eatf(lynx, h=10, level=95, type_pi = "A"))
plot(ahead::eatf(WWWusage, h=10, level=95, type_pi = "E"))
plot(ahead::eatf(Nile, h=10, level=95))
plot(ahead::eatf(fdeaths, h=10, level=95))


require(forecast)

## Not run: 

print(ahead::eatf(WWWusage, method = "EAT",
weights = c(0.5, 0, 0.5)))

print(ahead::eatf(WWWusage, method = "EAT"))


obj <- ahead::eatf(WWWusage, method = "EAT",
weights = c(0, 0.5, 0.5), h=10,
type_pi = "T")
plot(obj)


obj <- ahead::eatf(WWWusage, method = "EAT",
weights = c(0, 0.5, 0.5), h=10, type_pi="A")
plot(obj)

## End(Not run)


par(mfrow=c(3, 2))
plot(ahead::eatf(USAccDeaths, h=10, level=95))
plot(ahead::eatf(AirPassengers, h=10, level=95, type_pi = "T"))
plot(ahead::eatf(lynx, h=10, level=95, type_pi = "A"))
plot(ahead::eatf(WWWusage, h=10, level=95, type_pi = "E"))
plot(ahead::eatf(Nile, h=10, level=95))
plot(ahead::eatf(fdeaths, h=10, level=95))

Fit and forecast for benchmarking purposes

Usage

fitforecast(
  y,
  h = NULL,
  pct_train = 0.9,
  pct_calibration = 0.5,
  method = c("thetaf", "arima", "ets", "te", "tbats", "tslm", "dynrmf", "ridge2f",
    "naive", "snaive"),
  level = 95,
  B = 1000L,
  seed = 17223L,
  graph = TRUE,
  conformalize = FALSE,
  type_calibration = c("splitconformal", "cv1", "loocv"),
  gap = 3L,
  agg = c("mean", "median"),
  vol = c("constant", "garch"),
  type_sim = c("kde", "surrogate", "bootstrap"),
  ...
)
fitforecast(
  y,
  h = NULL,
  pct_train = 0.9,
  pct_calibration = 0.5,
  method = c("thetaf", "arima", "ets", "te", "tbats", "tslm", "dynrmf", "ridge2f",
    "naive", "snaive"),
  level = 95,
  B = 1000L,
  seed = 17223L,
  graph = TRUE,
  conformalize = FALSE,
  type_calibration = c("splitconformal", "cv1", "loocv"),
  gap = 3L,
  agg = c("mean", "median"),
  vol = c("constant", "garch"),
  type_sim = c("kde", "surrogate", "bootstrap"),
  ...
)

Arguments

`y`	A univariate time series of class `ts`
`h`	Forecasting horizon (default is `NULL`, in that case, `pct_train` and `pct_calibration` are used)
`pct_train`	Percentage of data in the training set, when `h` is `NULL`
`pct_calibration`	Percentage of data in the calibration set for conformal prediction
`method`	For now "thetaf" (default), "arima", "ets", "tbats", "tslm", "dynrmf" (from ahead), "ridge2f" (from ahead), "naive", "snaive"
`level`	Confidence level for prediction intervals in \item BNumber of bootstrap replications or number of simulations (yes, 'B' is unfortunate) \item seedReproducibility seed \item graphPlot or not? \item conformalizeCalibrate or not? \item type_calibration"splitconformal" (default conformal method), "cv1" (do not use), "loocv" (do not use) \item gaplength of training set for loocv conformal (do not use) \item agg"mean" or "median" (aggregation method) for \item vol"constant" or "garch" (type of volatility modeling for calibrated residuals) \item type_sim"kde", "surrogate", "bootstrap" (type of simulation for calibrated residuals) \item ...additional parameters

an object of class 'forecast' with additional information Fit and forecast for benchmarking purposes

par(mfrow=c(2, 2)) obj1 <- ahead::fitforecast(AirPassengers) obj2 <- ahead::fitforecast(AirPassengers, conformalize = TRUE) plot(AirPassengers) plot(obj1) obj2$plot() obj2$plot("simulations")

Calculate returns or log-returns for multivariate time series

Description

Calculate returns or log-returns for multivariate time series

Usage

getreturns(x, type = c("basic", "log"))
getreturns(x, type = c("basic", "log"))

Arguments

`x`	Multivariate time series
`type`	Type of return: basic return ("basic") or log-return ("log")

Value

The returns

Examples


returns <- getreturns(EuStockMarkets)
log_returns <- getreturns(EuStockMarkets,
                          type = "log")

par(mfrow=c(1, 3))
matplot(EuStockMarkets, type = 'l', main = "Closing Prices of \n European stocks (1991-1998)",
xlab = "time")
matplot(returns, type = 'l', main = "Returns", xlab = "time")
matplot(log_returns, type = 'l', main = "Log-returns", xlab = "time")

returns <- getreturns(EuStockMarkets)
log_returns <- getreturns(EuStockMarkets,
                          type = "log")

par(mfrow=c(1, 3))
matplot(EuStockMarkets, type = 'l', main = "Closing Prices of \n European stocks (1991-1998)",
xlab = "time")
matplot(returns, type = 'l', main = "Returns", xlab = "time")
matplot(log_returns, type = 'l', main = "Log-returns", xlab = "time")

Obtain simulations (when relevant) from a selected time series

Description

Obtain simulations (when relevant) from a selected time series

Usage

getsimulations(obj, selected_series, transpose = FALSE)
getsimulations(obj, selected_series, transpose = FALSE)

Arguments

`obj`	result from ridge2f (multivariate time series forecast with simulations)
`selected_series`	name of the time series selected
`transpose`	return a transposed time series

Examples


require(fpp)

obj <- ahead::ridge2f(fpp::insurance, h = 7,
                      type_pi = "bootstrap", B = 5)
print(getsimulations(obj, selected_series = "TV.advert"))
print(getsimulations(obj, selected_series = "Quotes"))
print(getsimulations(obj, selected_series = "TV.advert", transpose = TRUE))
print(getsimulations(obj, selected_series = "Quotes", transpose = TRUE))

require(fpp)

obj <- ahead::ridge2f(fpp::insurance, h = 7,
                      type_pi = "bootstrap", B = 5)
print(getsimulations(obj, selected_series = "TV.advert"))
print(getsimulations(obj, selected_series = "Quotes"))
print(getsimulations(obj, selected_series = "TV.advert", transpose = TRUE))
print(getsimulations(obj, selected_series = "Quotes", transpose = TRUE))

Loess forecasting

Description

Loess forecasting

Usage

loessf(
  y,
  h = 5,
  level = 95,
  span = 0.75,
  degree = 2,
  type_pi = c("bootstrap", "blockbootstrap", "movingblockbootstrap"),
  b = NULL,
  B = 250,
  type_aggregation = c("mean", "median"),
  seed = 123
)
loessf(
  y,
  h = 5,
  level = 95,
  span = 0.75,
  degree = 2,
  type_pi = c("bootstrap", "blockbootstrap", "movingblockbootstrap"),
  b = NULL,
  B = 250,
  type_aggregation = c("mean", "median"),
  seed = 123
)

Arguments

`y`	A numeric vector or time series of class `ts`
`h`	Forecasting horizon
`level`	Confidence level for prediction intervals
`span`	the parameter which controls the degree of smoothing
`degree`	the degree of the polynomials to be used, normally 1 or 2. (Degree 0 is also allowed, but see `stats::loess`)
`type_pi`	Type of prediction interval currently (independent) "bootstrap", (circular) "blockbootstrap", or "movingblockbootstrap"
`b`	block length for circular block bootstrap
`B`	number of bootstrap replications
`type_aggregation`	Type of aggregation, ONLY for bootstrapping; either "mean" or "median"
`seed`	reproducibility seed

Value

An object of class "forecast"; a list containing the following elements:

`model`	A list containing information about the fitted model
`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`x`	The original time series
`residuals`	Residuals from the fitted model
`sims`	Model simulations for bootstrapping

Examples


par(mfrow = c(3, 1))

plot(loessf(Nile, h=20, level=95, B=10))

plot(loessf(Nile, h=20, level=95, B=10,
     type_pi = "blockbootstrap"))

plot(loessf(Nile, h=20, level=95, B=10,
     type_pi = "movingblockbootstrap"))

par(mfrow = c(3, 1))

plot(loessf(Nile, h=20, level=95, B=10))

plot(loessf(Nile, h=20, level=95, B=10,
     type_pi = "blockbootstrap"))

plot(loessf(Nile, h=20, level=95, B=10,
     type_pi = "movingblockbootstrap"))

LOOCV for Ridge2 model

Description

LOOCV for Random Vector functional link network model with 2 regularization parameters

Usage

loocvridge2f(
  y,
  xreg = NULL,
  h = 5,
  level = 95,
  lags = 1,
  nb_hidden = 5,
  nodes_sim = c("sobol", "halton", "unif"),
  activ = c("relu", "sigmoid", "tanh", "leakyrelu", "elu", "linear"),
  a = 0.01,
  lambda_1 = 0.1,
  lambda_2 = 0.1,
  dropout = 0,
  type_forecast = c("recursive", "direct"),
  type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap",
    "rvinecopula", "splitconformal"),
  block_length = NULL,
  margins = c("gaussian", "empirical", "student"),
  seed = 1,
  B = 100L,
  type_aggregation = c("mean", "median"),
  centers = NULL,
  type_clustering = c("kmeans", "hclust"),
  ym = NULL,
  cl = 1L,
  show_progress = TRUE,
  ...
)
loocvridge2f(
  y,
  xreg = NULL,
  h = 5,
  level = 95,
  lags = 1,
  nb_hidden = 5,
  nodes_sim = c("sobol", "halton", "unif"),
  activ = c("relu", "sigmoid", "tanh", "leakyrelu", "elu", "linear"),
  a = 0.01,
  lambda_1 = 0.1,
  lambda_2 = 0.1,
  dropout = 0,
  type_forecast = c("recursive", "direct"),
  type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap",
    "rvinecopula", "splitconformal"),
  block_length = NULL,
  margins = c("gaussian", "empirical", "student"),
  seed = 1,
  B = 100L,
  type_aggregation = c("mean", "median"),
  centers = NULL,
  type_clustering = c("kmeans", "hclust"),
  ym = NULL,
  cl = 1L,
  show_progress = TRUE,
  ...
)

Arguments

`y`	A multivariate time series of class `ts` (preferred) or a `matrix`
`xreg`	External regressors. A data.frame (preferred) or a `matrix`
`h`	Forecasting horizon
`level`	Confidence level for prediction intervals
`lags`	Number of lags
`nb_hidden`	Number of nodes in hidden layer
`nodes_sim`	Type of simulation for nodes in the hidden layer
`activ`	Activation function
`a`	Hyperparameter for activation function "leakyrelu", "elu"
`lambda_1`	Regularization parameter for original predictors
`lambda_2`	Regularization parameter for transformed predictors
`dropout`	dropout regularization parameter (dropping nodes in hidden layer)
`type_forecast`	Recursive or direct forecast
`type_pi`	Type of prediction interval currently "gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap", "splitconformal" (very experimental right now), "rvinecopula" (with Gaussian margins for now, Student-t coming soon)
`block_length`	Length of block for circular or moving block bootstrap
`margins`	Distribution of margins: "gaussian", "empirical", "student" (postponed or never) for `type_pi == "rvinecopula"`
`seed`	Reproducibility seed for random stuff
`B`	Number of bootstrap replications or number of simulations (yes, 'B' is unfortunate)
`type_aggregation`	Type of aggregation, ONLY for bootstrapping; either "mean" or "median"
`centers`	Number of clusters for `type_clustering`
`type_clustering`	"kmeans" (K-Means clustering) or "hclust" (Hierarchical clustering)
`ym`	Univariate time series (`stats::ts`) of yield to maturities with `frequency = frequency(y)` and `start = tsp(y)[2] + 1 / frequency(y)`. Default is `NULL`.
`cl`	An integer; the number of clusters for parallel execution, for bootstrap
`show_progress`	A boolean; show progress bar for bootstrapping? Default is TRUE.
`...`	Additional parameters to be passed to `kmeans` or `hclust`

Value

An object of class "mtsforecast"; a list containing the following elements:

`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`sims`	Model simulations for bootstrapping (basic, or block)
`x`	The original time series
`residuals`	Residuals from the fitted model
`coefficients`	Regression coefficients for `type_pi == 'gaussian'` for now

Author(s)

T. Moudiki

References

Moudiki, T., Planchet, F., & Cousin, A. (2018). Multiple time series forecasting using quasi-randomized functional link neural networks. Risks, 6(1), 22.

Examples


require(fpp)

print(ahead::loocvridge2f(fpp::insurance))
print(ahead::loocvridge2f(fpp::usconsumption))

#foo <- function(xx) ahead::loocvridge2f(fpp::insurance, lambda_1=10^xx[1], lambda_2=10^xx[2])
#(opt <- stats::nlminb(objective=foo, lower=c(-10,-10), upper=c(10,10), start=c(0, 0)))
#print(ahead::loocvridge2f(fpp::insurance, lambda_1=10^opt$par[1], lambda_2=10^opt$par[2]))

require(fpp)

print(ahead::loocvridge2f(fpp::insurance))
print(ahead::loocvridge2f(fpp::usconsumption))

#foo <- function(xx) ahead::loocvridge2f(fpp::insurance, lambda_1=10^xx[1], lambda_2=10^xx[2])
#(opt <- stats::nlminb(objective=foo, lower=c(-10,-10), upper=c(10,10), start=c(0, 0)))
#print(ahead::loocvridge2f(fpp::insurance, lambda_1=10^opt$par[1], lambda_2=10^opt$par[2]))

Plot multivariate time series forecast or residuals

Description

Plot multivariate time series forecast or residuals

Usage

## S3 method for class 'mtsforecast'
plot(x, selected_series, type = c("pi", "dist", "sims"), level = 95, ...)
## S3 method for class 'mtsforecast'
plot(x, selected_series, type = c("pi", "dist", "sims"), level = 95, ...)

Arguments

`x`	result from `basicf`, `ridge2f` or `varf` (multivariate time series forecast)
`selected_series`	name of the time series selected for plotting
`type`	"pi": basic prediction intervals; "dist": a distribution of predictions; "sims": the simulations
`level`	confidence levels for prediction intervals
`...`	additional parameters to be passed to `plot` or `matplot`

Examples


require(fpp)

fit_obj_VAR <- ahead::varf(fpp::insurance, lags = 2,
h = 10, level = 95)

fit_obj_ridge2 <- ahead::ridge2f(fpp::insurance, lags = 2,
h = 10, level = 95)

par(mfrow=c(2, 2))
plot(fit_obj_VAR, "Quotes")
plot(fit_obj_VAR, "TV.advert")
plot(fit_obj_ridge2, "Quotes")
plot(fit_obj_ridge2, "TV.advert")

obj <- ahead::ridge2f(fpp::insurance, h = 10, type_pi = "blockbootstrap",
block_length=5, B = 10)
par(mfrow=c(1, 2))
plot(obj, selected_series = "Quotes", type = "sims",
main = "Predictive simulation for Quotes")
plot(obj, selected_series = "TV.advert", type = "sims",
main = "Predictive simulation for TV.advert")


par(mfrow=c(1, 2))
plot(obj, selected_series = "Quotes", type = "dist",
main = "Predictive simulation for Quotes")
plot(obj, selected_series = "TV.advert", type = "dist",
main = "Predictive simulation for TV.advert")


require(fpp)

fit_obj_VAR <- ahead::varf(fpp::insurance, lags = 2,
h = 10, level = 95)

fit_obj_ridge2 <- ahead::ridge2f(fpp::insurance, lags = 2,
h = 10, level = 95)

par(mfrow=c(2, 2))
plot(fit_obj_VAR, "Quotes")
plot(fit_obj_VAR, "TV.advert")
plot(fit_obj_ridge2, "Quotes")
plot(fit_obj_ridge2, "TV.advert")

obj <- ahead::ridge2f(fpp::insurance, h = 10, type_pi = "blockbootstrap",
block_length=5, B = 10)
par(mfrow=c(1, 2))
plot(obj, selected_series = "Quotes", type = "sims",
main = "Predictive simulation for Quotes")
plot(obj, selected_series = "TV.advert", type = "sims",
main = "Predictive simulation for TV.advert")


par(mfrow=c(1, 2))
plot(obj, selected_series = "Quotes", type = "dist",
main = "Predictive simulation for Quotes")
plot(obj, selected_series = "TV.advert", type = "dist",
main = "Predictive simulation for TV.advert")

Ridge2 model

Description

Random Vector functional link network model with 2 regularization parameters

Usage

ridge2f(
  y,
  h = 5,
  level = 95,
  xreg = NULL,
  lags = 1,
  nb_hidden = 5,
  nodes_sim = c("sobol", "halton", "unif"),
  activ = c("relu", "sigmoid", "tanh", "leakyrelu", "elu", "linear"),
  a = 0.01,
  lambda_1 = 0.1,
  lambda_2 = 0.1,
  dropout = 0,
  type_forecast = c("recursive", "direct"),
  type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap",
    "rvinecopula"),
  block_length = NULL,
  margins = c("gaussian", "empirical"),
  seed = 1,
  B = 100L,
  type_aggregation = c("mean", "median"),
  centers = NULL,
  type_clustering = c("kmeans", "hclust"),
  ym = NULL,
  cl = 1L,
  show_progress = TRUE,
  ...
)
ridge2f(
  y,
  h = 5,
  level = 95,
  xreg = NULL,
  lags = 1,
  nb_hidden = 5,
  nodes_sim = c("sobol", "halton", "unif"),
  activ = c("relu", "sigmoid", "tanh", "leakyrelu", "elu", "linear"),
  a = 0.01,
  lambda_1 = 0.1,
  lambda_2 = 0.1,
  dropout = 0,
  type_forecast = c("recursive", "direct"),
  type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap",
    "rvinecopula"),
  block_length = NULL,
  margins = c("gaussian", "empirical"),
  seed = 1,
  B = 100L,
  type_aggregation = c("mean", "median"),
  centers = NULL,
  type_clustering = c("kmeans", "hclust"),
  ym = NULL,
  cl = 1L,
  show_progress = TRUE,
  ...
)

Arguments

`y`	A univariate of multivariate time series of class `ts` (preferred) or a `matrix`
`h`	Forecasting horizon
`level`	Confidence level for prediction intervals
`xreg`	External regressors. A data.frame (preferred) or a `matrix`
`lags`	Number of lags
`nb_hidden`	Number of nodes in hidden layer
`nodes_sim`	Type of simulation for nodes in the hidden layer
`activ`	Activation function
`a`	Hyperparameter for activation function "leakyrelu", "elu"
`lambda_1`	Regularization parameter for original predictors
`lambda_2`	Regularization parameter for transformed predictors
`dropout`	dropout regularization parameter (dropping nodes in hidden layer)
`type_forecast`	Recursive or direct forecast
`type_pi`	Type of prediction interval currently "gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap", "rvinecopula" (with Gaussian and empirical margins for now)
`block_length`	Length of block for circular or moving block bootstrap
`margins`	Distribution of margins: "gaussian", "empirical" for `type_pi == "rvinecopula"`
`seed`	Reproducibility seed for random stuff
`B`	Number of bootstrap replications or number of simulations (yes, 'B' is unfortunate)
`type_aggregation`	Type of aggregation, ONLY for bootstrapping; either "mean" or "median"
`centers`	Number of clusters for `type_clustering`
`type_clustering`	"kmeans" (K-Means clustering) or "hclust" (Hierarchical clustering)
`ym`	Univariate time series (`stats::ts`) of yield to maturities with `frequency = frequency(y)` and `start = tsp(y)[2] + 1 / frequency(y)`. Default is `NULL`.
`cl`	An integer; the number of clusters for parallel execution, for bootstrap
`show_progress`	A boolean; show progress bar for bootstrapping? Default is TRUE.
`...`	Additional parameters to be passed to `kmeans` or `hclust`

Value

An object of class "mtsforecast"; a list containing the following elements:

`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`sims`	Model simulations for bootstrapping (basic, or block)
`x`	The original time series
`residuals`	Residuals from the fitted model
`coefficients`	Regression coefficients for `type_pi == 'gaussian'` for now

Author(s)

T. Moudiki

References

Moudiki, T., Planchet, F., & Cousin, A. (2018). Multiple time series forecasting using quasi-randomized functional link neural networks. Risks, 6(1), 22.

Examples


require(fpp)

print(ahead::ridge2f(fpp::insurance)$mean)
print(ahead::ridge2f(fpp::usconsumption)$lower)

res <- ahead::ridge2f(fpp::insurance, h=10, lags=2)
par(mfrow=c(1, 2))
plot(res, "Quotes")
plot(res, "TV.advert")

# include a trend (just for the example)
xreg <- as.numeric(time(fpp::insurance))
res2 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
h=10, lags=2)
par(mfrow=c(1, 2))
plot(res2, "Quotes")
plot(res2, "TV.advert")

# block bootstrap
xreg <- as.numeric(time(fpp::insurance))
res3 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
                      h=10, lags=1L, type_pi = "bootstrap", B=10)
res5 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
                      h=10, lags=1L, type_pi = "blockbootstrap", B=10,
                      block_length = 4)

print(res3$sims[[2]])
print(res5$sims[[2]])

par(mfrow=c(2, 2))
plot(res3, "Quotes")
plot(res3, "TV.advert")
plot(res5, "Quotes")
plot(res5, "TV.advert")


res4 <- ahead::ridge2f(fpp::usconsumption, h=20, lags=2L,
lambda_2=1)
par(mfrow=c(1, 2))
plot(res4, "income")
plot(res4, "consumption")


# moving block bootstrap
xreg <- as.numeric(time(fpp::insurance))
res6 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
                      h=10, lags=1L,
                      type_pi = "movingblockbootstrap", B=10,
                      block_length = 4)

print(res6$sims[[2]])

par(mfrow=c(1, 2))
plot(res6, "Quotes")
plot(res6, "TV.advert")


require(fpp)

print(ahead::ridge2f(fpp::insurance)$mean)
print(ahead::ridge2f(fpp::usconsumption)$lower)

res <- ahead::ridge2f(fpp::insurance, h=10, lags=2)
par(mfrow=c(1, 2))
plot(res, "Quotes")
plot(res, "TV.advert")

# include a trend (just for the example)
xreg <- as.numeric(time(fpp::insurance))
res2 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
h=10, lags=2)
par(mfrow=c(1, 2))
plot(res2, "Quotes")
plot(res2, "TV.advert")

# block bootstrap
xreg <- as.numeric(time(fpp::insurance))
res3 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
                      h=10, lags=1L, type_pi = "bootstrap", B=10)
res5 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
                      h=10, lags=1L, type_pi = "blockbootstrap", B=10,
                      block_length = 4)

print(res3$sims[[2]])
print(res5$sims[[2]])

par(mfrow=c(2, 2))
plot(res3, "Quotes")
plot(res3, "TV.advert")
plot(res5, "Quotes")
plot(res5, "TV.advert")


res4 <- ahead::ridge2f(fpp::usconsumption, h=20, lags=2L,
lambda_2=1)
par(mfrow=c(1, 2))
plot(res4, "income")
plot(res4, "consumption")


# moving block bootstrap
xreg <- as.numeric(time(fpp::insurance))
res6 <- ahead::ridge2f(fpp::insurance, xreg=xreg,
                      h=10, lags=1L,
                      type_pi = "movingblockbootstrap", B=10,
                      block_length = 4)

print(res6$sims[[2]])

par(mfrow=c(1, 2))
plot(res6, "Quotes")
plot(res6, "TV.advert")

Vector Autoregressive model (adapted from vars::VAR)

Description

Vector Autoregressive model adapted from vars::VAR (only for benchmarking)

Usage

varf(
  y,
  h = 5,
  level = 95,
  lags = 1,
  type_VAR = c("const", "trend", "both", "none"),
  ...
)
varf(
  y,
  h = 5,
  level = 95,
  lags = 1,
  type_VAR = c("const", "trend", "both", "none"),
  ...
)

Arguments

`y`	A multivariate time series of class `ts`
`h`	Forecasting horizon
`level`	Confidence level for prediction intervals
`lags`	Number of lags
`type_VAR`	Type of deterministic regressors to include.
`...`	Additional parameters to be passed to vars::VAR.

Value

An object of class "mtsforecast"; a list containing the following elements:

`method`	The name of the forecasting method as a character string
`mean`	Point forecasts for the time series
`lower`	Lower bound for prediction interval
`upper`	Upper bound for prediction interval
`x`	The original time series
`residuals`	Residuals from the fitted model

Author(s)

T. Moudiki

References

Bernhard Pfaff (2008). VAR, SVAR and SVEC Models: Implementation Within R Package vars. Journal of Statistical Software 27(4). URL http://www.jstatsoft.org/v27/i04/.

Pfaff, B. (2008) Analysis of Integrated and Cointegrated Time Series with R. Second Edition. Springer, New York. ISBN 0-387-27960-1

Examples


require(fpp)

print(varf(fpp::insurance, lags=2, h=10))

res <- varf(fpp::usconsumption, h=20, lags=2)

par(mfrow=c(1, 2))
plot(res, "consumption")
plot(res, "income")

require(fpp)

print(varf(fpp::insurance, lags=2, h=10))

res <- varf(fpp::usconsumption, h=20, lags=2)

par(mfrow=c(1, 2))
plot(res, "consumption")
plot(res, "income")

Package 'ahead'

Help Index

ARMA(1, 1)-GARCH(1, 1) forecasting (with simulation)

Description

Usage

Arguments

Value

Author(s)

Examples

Basic forecasting (mean, median, random walk)

Description

Usage

Arguments

Value

Examples

Create trend and seasonality features for univariate time series

Description

Usage

Arguments

Value

Examples

Dynamic regression model

Description

Usage

Arguments

Value

Author(s)

References

Examples

Combined ets-arima-theta forecasts

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Fit and forecast for benchmarking purposes

Usage

Arguments

Calculate returns or log-returns for multivariate time series

Description

Usage

Arguments

Value

Examples

Obtain simulations (when relevant) from a selected time series

Description

Usage

Arguments

Examples

Loess forecasting

Description

Usage

Arguments

Value

Examples

LOOCV for Ridge2 model

Description

Usage

Arguments

Value

Author(s)

References

Examples

Plot multivariate time series forecast or residuals

Description

Usage

Arguments

Examples

Ridge2 model

Description

Usage

Arguments

Value

Author(s)

References

Examples

Vector Autoregressive model (adapted from vars::VAR)