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data("LakeHuron")
years <- time(LakeHuron)
fit <- fastTS(LakeHuron, n_lags_max = 3)
fit
#> An endogenous PACF-based fastTS model.
#>
#> PF_gamma AICc_d BIC_d
#> 0.00 *0* 0.54
#> 0.25 <0.01 0.54
#> 0.50 0.01 0.55
#> 1.00 0.05 0.28
#> 2.00 0.66 *0*
#> 4.00 4.46 0.89
#> 8.00 4.46 0.89
#> 16.00 4.46 0.89
#>
#> AICc_d and BIC_d are the difference from the minimum; *0* is best.
#>
#> - Best AICc model: 4 active terms
#> - Best BIC model: 3 active terms
#>
#> Test-set prediction accuracy (20% held-out test set)
#> rmse rsq mae
#> AICc 0.7836646 0.5955089 0.6056737
#> BIC 0.7486619 0.6308355 0.6032140predict do?Let \(y_t\) refer to our outcome series, and \(\hat y_t^{(k)}\) refer to the \(k\)-step-ahead prediction for \(y_t\).
The predicted value returned at any time point \(t\) is the model’s prediction for that
point \(\hat y_t\), given the model and
all data up to \(t -\)
n_ahead. This means that
The 1-step prediction \(\hat y_t^{(1)}\) is computed by using lags of \(y_t\) deemed important by the fitting process.
The 2-step prediction \(\hat y_t^{(2)}\) is computed by using important lags of \(y_t\), but replacing the first lag \(y_{t-1}\) with \(\hat y_{t-1}^{(1)}\).
The 3-step prediction \(\hat y_t^{(3)}\) is computed by replacing the first lag \(y_{t-1}\) with \(\hat y_{t-1}^{(2)}\) and the second lag \(y_{t-2}\) with \(\hat y_{t-2}^{(1)}\).
And so on until the \(k\)-step prediction \(\hat y_t^{(k)}\) is similarly computed by replacing lags of \(y_t\) with predicted values as necessary.
Here is an example with the LakeHuron data set.
p1 <- predict(fit, n_ahead = 1)
p7 <- predict(fit, n_ahead = 7)
predictions <- tibble(years, LakeHuron, p1, p7)
head(predictions, 10)
#> # A tibble: 10 × 4
#> years LakeHuron p1 p7
#> <dbl> <dbl> <dbl> <dbl>
#> 1 1875 580. NA NA
#> 2 1876 582. NA NA
#> 3 1877 581. NA NA
#> 4 1878 581. 580. NA
#> 5 1879 580. 581. NA
#> 6 1880 580. 579. NA
#> 7 1881 580. 581. NA
#> 8 1882 581. 580. NA
#> 9 1883 581. 581. NA
#> 10 1884 581. 581. 579.
tail(predictions)
#> # A tibble: 6 × 4
#> years LakeHuron p1 p7
#> <dbl> <dbl> <dbl> <dbl>
#> 1 1967 578. 578. 579.
#> 2 1968 579. 579. 579.
#> 3 1969 580. 579. 579.
#> 4 1970 579. 580. 579.
#> 5 1971 580. 579. 578.
#> 6 1972 580. 580. 579.predict function returns missing values for the
first n_lags_max observations for 1-step ahead predictions.
The prediction process back-fill real values when necessary for early
predictions, but resets to NA before returning predictions.Note: there is a “burn-in” component to fastTS objects
that means the first n_lags_max observations are
back-filled in.
By default, the predict function does
not produce forecasts. In order to get forecasts, we
need to set forecast_ahead = TRUE, which will return
forecasted values at the tail end of the returned vector.
p1 <- predict(fit, n_ahead = 1, forecast_ahead = TRUE)
predictions <- tibble(time = c(1973), p1)
# For 7-step ahead forecasts
p7 <- predict(fit, n_ahead = 7, forecast_ahead = TRUE)
predictions <- tibble(time = c(1973:1979), p7)
predictions
#> # A tibble: 7 × 2
#> time p7
#> <int> <dbl>
#> 1 1973 580.
#> 2 1974 580.
#> 3 1975 579.
#> 4 1976 579.
#> 5 1977 579.
#> 6 1978 579.
#> 7 1979 579.Finally, the return_intermediate option allows users to
collect all of the step-ahead predictions up to \(k\):
p1_p7 <- predict(fit, n_ahead = 7, return_intermediate = TRUE)
predictions <- tibble(years, LakeHuron, p1_p7)
tail(predictions)
#> # A tibble: 6 × 9
#> years LakeHuron p1 p2 p3 p4 p5 p6 p7
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1967 578. 578. 578. 578. 578. 579. 579. 579.
#> 2 1968 579. 579. 578. 578. 578. 578. 579. 579.
#> 3 1969 580. 579. 579. 578. 578. 578. 578. 579.
#> 4 1970 579. 580. 579. 579. 578. 578. 578. 579.
#> 5 1971 580. 579. 580. 579. 579. 578. 578. 578.
#> 6 1972 580. 580. 579. 579. 579. 579. 579. 579.These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.