Forecasting functions for seasonal ARIMA models

Forecasting functions for seasonal ARIMA models.

Usage

fun.forecast(past, n = max(2 * length(past), 12), eps = numeric(n), pasteps, ...)

Arguments

past: past values of the time series, by default zeroes.
n: number of forecasts to compute.
eps: values of the white noise sequence (for simulation of future). Currently not used!
pasteps: past values of the white noise sequence for models with MA terms, 0 by default.
...: specification of the model, passed to new() to create a "SarimaModel" object, see Details.

Details

fun.forecast computes predictions from a SARIMA model. The model is specified using the "..." arguments which are passed to new("SarimaModel", ...), see the description of class "SarimaModel" for details.

Argument past, if provided, should contain a least as many values as needed for the prediction equation. It is harmless to provide more values than necessary, even a whole time series.

fun.forecast can be used to illustrate, for example, the inherent difference for prediction of integrated and seasonally integrated models to corresponding models with roots close to the unit circle.

Value

the forecasts as an object of class "ts"

Author

Georgi N. Boshnakov

Examples

f1 <- fun.forecast(past = 1, n = 100, ar = c(0.85), center = 5)
plot(f1)


f2 <- fun.forecast(past = 8, n = 100, ar = c(0.85), center = 5)
plot(f2)


f3 <- fun.forecast(past = 10, n = 100, ar = c(-0.85), center = 5)
plot(f3)


frw1 <- fun.forecast(past = 1, n = 100, iorder = 1)
plot(frw1)


frw2 <- fun.forecast(past = 3, n = 100, iorder = 1)
plot(frw2)


frwa1 <- fun.forecast(past = c(1, 2), n = 100, ar = c(0.85), iorder = 1)
plot(frwa1)


fi2a <- fun.forecast(past = c(3, 1), n = 100, iorder = 2)
plot(fi2a)


fi2b <- fun.forecast(past = c(1, 3), n = 100, iorder = 2)
plot(fi2b)


fari1p2 <- fun.forecast(past = c(0, 1, 3), ar = c(0.9), n = 20, iorder = 2)
plot(fari1p2)


fsi1 <- fun.forecast(past = rnorm(4), n = 100, siorder = 1, nseasons = 4)
plot(fsi1)


fexa <- fun.forecast(past = rnorm(5), n = 100, ar = c(0.85), siorder = 1,
                     nseasons = 4)
plot(fexa)


fi2a <- fun.forecast(past = rnorm(24, sd = 5), n = 120, siorder = 2,
                     nseasons = 12)
plot(fi2a)


fi1si1a <- fun.forecast(past = rnorm(24, sd = 5), n = 120, iorder = 1,
                        siorder = 1, nseasons = 12)
plot(fi1si1a)


fi1si1a <- fun.forecast(past = AirPassengers[120:144], n = 120, iorder = 1,
                        siorder = 1, nseasons = 12)
plot(fi1si1a)


m1 <- list(iorder = 1, siorder = 1, ma = 0.8, nseasons = 12, sigma2 = 1)
m1
#> $iorder
#> [1] 1
#> 
#> $siorder
#> [1] 1
#> 
#> $ma
#> [1] 0.8
#> 
#> $nseasons
#> [1] 12
#> 
#> $sigma2
#> [1] 1
#> 
x <- sim_sarima(model = m1, n = 500)
acf(diff(diff(x), lag = 12), lag.max = 96)

pacf(diff(diff(x), lag = 12), lag.max = 96)


m2 <- list(iorder = 1, siorder = 1, ma = 0.8, sma = 0.5, nseasons = 12,
           sigma2 = 1)
m2
#> $iorder
#> [1] 1
#> 
#> $siorder
#> [1] 1
#> 
#> $ma
#> [1] 0.8
#> 
#> $sma
#> [1] 0.5
#> 
#> $nseasons
#> [1] 12
#> 
#> $sigma2
#> [1] 1
#> 
x2 <- sim_sarima(model = m2, n = 500)
acf(diff(diff(x2), lag = 12), lag.max = 96)

pacf(diff(diff(x2), lag = 12), lag.max = 96)

fit2 <- arima(x2, order = c(0, 1, 1),
              seasonal = list(order = c(0, 1, 0), nseasons = 12))
fit2
#> 
#> Call:
#> arima(x = x2, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 0), nseasons = 12))
#> 
#> Coefficients:
#>           ma1
#>       -0.9844
#> s.e.   0.0058
#> 
#> sigma^2 estimated as 38.83:  log likelihood = -1619.52,  aic = 3243.05
tsdiag(fit2)

tsdiag(fit2, gof.lag = 96)


x2past <- rnorm(13, sd = 10)
x2 <- sim_sarima(model = m2, n = 500, x = list(init = x2past))
plot(x2)


fun.forecast(ar = 0.5, n = 100)
#> Time Series:
#> Start = 1 
#> End = 100 
#> Frequency = 1 
#>   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
fun.forecast(ar = 0.5, n = 100, past = 1)
#> Time Series:
#> Start = 1 
#> End = 100 
#> Frequency = 1 
#>   [1] 5.000000e-01 2.500000e-01 1.250000e-01 6.250000e-02 3.125000e-02
#>   [6] 1.562500e-02 7.812500e-03 3.906250e-03 1.953125e-03 9.765625e-04
#>  [11] 4.882812e-04 2.441406e-04 1.220703e-04 6.103516e-05 3.051758e-05
#>  [16] 1.525879e-05 7.629395e-06 3.814697e-06 1.907349e-06 9.536743e-07
#>  [21] 4.768372e-07 2.384186e-07 1.192093e-07 5.960464e-08 2.980232e-08
#>  [26] 1.490116e-08 7.450581e-09 3.725290e-09 1.862645e-09 9.313226e-10
#>  [31] 4.656613e-10 2.328306e-10 1.164153e-10 5.820766e-11 2.910383e-11
#>  [36] 1.455192e-11 7.275958e-12 3.637979e-12 1.818989e-12 9.094947e-13
#>  [41] 4.547474e-13 2.273737e-13 1.136868e-13 5.684342e-14 2.842171e-14
#>  [46] 1.421085e-14 7.105427e-15 3.552714e-15 1.776357e-15 8.881784e-16
#>  [51] 4.440892e-16 2.220446e-16 1.110223e-16 5.551115e-17 2.775558e-17
#>  [56] 1.387779e-17 6.938894e-18 3.469447e-18 1.734723e-18 8.673617e-19
#>  [61] 4.336809e-19 2.168404e-19 1.084202e-19 5.421011e-20 2.710505e-20
#>  [66] 1.355253e-20 6.776264e-21 3.388132e-21 1.694066e-21 8.470329e-22
#>  [71] 4.235165e-22 2.117582e-22 1.058791e-22 5.293956e-23 2.646978e-23
#>  [76] 1.323489e-23 6.617445e-24 3.308722e-24 1.654361e-24 8.271806e-25
#>  [81] 4.135903e-25 2.067952e-25 1.033976e-25 5.169879e-26 2.584939e-26
#>  [86] 1.292470e-26 6.462349e-27 3.231174e-27 1.615587e-27 8.077936e-28
#>  [91] 4.038968e-28 2.019484e-28 1.009742e-28 5.048710e-29 2.524355e-29
#>  [96] 1.262177e-29 6.310887e-30 3.155444e-30 1.577722e-30 7.888609e-31
fun.forecast(ma = 0.5, n = 100, past = 1)
#> Time Series:
#> Start = 1 
#> End = 101 
#> Frequency = 1 
#>   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
fun.forecast(iorder = 1, ma = 0.5, n = 100, past = 1)
#> Time Series:
#> Start = 1 
#> End = 101 
#> Frequency = 1 
#>   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
fun.forecast(iorder = 1, ma = 0.5, ar = 0.8, n = 100, past = 1)
#> Time Series:
#> Start = 1 
#> End = 100 
#> Frequency = 1 
#>   [1] 8.000000e-01 6.400000e-01 5.120000e-01 4.096000e-01 3.276800e-01
#>   [6] 2.621440e-01 2.097152e-01 1.677722e-01 1.342177e-01 1.073742e-01
#>  [11] 8.589935e-02 6.871948e-02 5.497558e-02 4.398047e-02 3.518437e-02
#>  [16] 2.814750e-02 2.251800e-02 1.801440e-02 1.441152e-02 1.152922e-02
#>  [21] 9.223372e-03 7.378698e-03 5.902958e-03 4.722366e-03 3.777893e-03
#>  [26] 3.022315e-03 2.417852e-03 1.934281e-03 1.547425e-03 1.237940e-03
#>  [31] 9.903520e-04 7.922816e-04 6.338253e-04 5.070602e-04 4.056482e-04
#>  [36] 3.245186e-04 2.596148e-04 2.076919e-04 1.661535e-04 1.329228e-04
#>  [41] 1.063382e-04 8.507059e-05 6.805647e-05 5.444518e-05 4.355614e-05
#>  [46] 3.484491e-05 2.787593e-05 2.230075e-05 1.784060e-05 1.427248e-05
#>  [51] 1.141798e-05 9.134385e-06 7.307508e-06 5.846007e-06 4.676805e-06
#>  [56] 3.741444e-06 2.993155e-06 2.394524e-06 1.915619e-06 1.532496e-06
#>  [61] 1.225996e-06 9.807971e-07 7.846377e-07 6.277102e-07 5.021681e-07
#>  [66] 4.017345e-07 3.213876e-07 2.571101e-07 2.056881e-07 1.645505e-07
#>  [71] 1.316404e-07 1.053123e-07 8.424983e-08 6.739987e-08 5.391989e-08
#>  [76] 4.313591e-08 3.450873e-08 2.760699e-08 2.208559e-08 1.766847e-08
#>  [81] 1.413478e-08 1.130782e-08 9.046257e-09 7.237006e-09 5.789604e-09
#>  [86] 4.631684e-09 3.705347e-09 2.964277e-09 2.371422e-09 1.897138e-09
#>  [91] 1.517710e-09 1.214168e-09 9.713344e-10 7.770676e-10 6.216540e-10
#>  [96] 4.973232e-10 3.978586e-10 3.182869e-10 2.546295e-10 2.037036e-10

fun.forecast(m1, n = 100)
#> Time Series:
#> Start = 1 
#> End = 101 
#> Frequency = 1 
#> $sigma2
#> [1] 0
#> 
#> [[2]]
#> [1] 0
#> 
#> [[3]]
#> [1] 0
#> 
#> [[4]]
#> [1] 0
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#> [1] 0
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#> [1] 0
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#> [1] 0
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#> [1] 0
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#> [1] 0
#> 
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#> [1] 0
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#> [1] 0
#> 
fun.forecast(m2, n = 100)
#> Time Series:
#> Start = 1 
#> End = 101 
#> Frequency = 1 
#> $sigma2
#> [1] 0
#> 
#> [[2]]
#> [1] 0
#> 
#> [[3]]
#> [1] 0
#> 
#> [[4]]
#> [1] 0
#> 
#> [[5]]
#> [1] 0
#> 
#> [[6]]
#> [1] 0
#> 
#> [[7]]
#> [1] 0
#> 
#> [[8]]
#> [1] 0
#> 
#> [[9]]
#> [1] 0
#> 
#> [[10]]
#> [1] 0
#> 
#> [[11]]
#> [1] 0
#> 
#> [[12]]
#> [1] 0
#> 
#> [[13]]
#> [1] 0
#> 
#> [[14]]
#> [1] 0
#> 
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#> [1] 0
#> 
#> [[16]]
#> [1] 0
#> 
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#> 
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#> [1] 0
#> 
fun.forecast(iorder = 1, ar = 0.8, ma = 0.5, n = 100, past = 1)
#> Time Series:
#> Start = 1 
#> End = 100 
#> Frequency = 1 
#>   [1] 8.000000e-01 6.400000e-01 5.120000e-01 4.096000e-01 3.276800e-01
#>   [6] 2.621440e-01 2.097152e-01 1.677722e-01 1.342177e-01 1.073742e-01
#>  [11] 8.589935e-02 6.871948e-02 5.497558e-02 4.398047e-02 3.518437e-02
#>  [16] 2.814750e-02 2.251800e-02 1.801440e-02 1.441152e-02 1.152922e-02
#>  [21] 9.223372e-03 7.378698e-03 5.902958e-03 4.722366e-03 3.777893e-03
#>  [26] 3.022315e-03 2.417852e-03 1.934281e-03 1.547425e-03 1.237940e-03
#>  [31] 9.903520e-04 7.922816e-04 6.338253e-04 5.070602e-04 4.056482e-04
#>  [36] 3.245186e-04 2.596148e-04 2.076919e-04 1.661535e-04 1.329228e-04
#>  [41] 1.063382e-04 8.507059e-05 6.805647e-05 5.444518e-05 4.355614e-05
#>  [46] 3.484491e-05 2.787593e-05 2.230075e-05 1.784060e-05 1.427248e-05
#>  [51] 1.141798e-05 9.134385e-06 7.307508e-06 5.846007e-06 4.676805e-06
#>  [56] 3.741444e-06 2.993155e-06 2.394524e-06 1.915619e-06 1.532496e-06
#>  [61] 1.225996e-06 9.807971e-07 7.846377e-07 6.277102e-07 5.021681e-07
#>  [66] 4.017345e-07 3.213876e-07 2.571101e-07 2.056881e-07 1.645505e-07
#>  [71] 1.316404e-07 1.053123e-07 8.424983e-08 6.739987e-08 5.391989e-08
#>  [76] 4.313591e-08 3.450873e-08 2.760699e-08 2.208559e-08 1.766847e-08
#>  [81] 1.413478e-08 1.130782e-08 9.046257e-09 7.237006e-09 5.789604e-09
#>  [86] 4.631684e-09 3.705347e-09 2.964277e-09 2.371422e-09 1.897138e-09
#>  [91] 1.517710e-09 1.214168e-09 9.713344e-10 7.770676e-10 6.216540e-10
#>  [96] 4.973232e-10 3.978586e-10 3.182869e-10 2.546295e-10 2.037036e-10