Lake Huron data set
data("LakeHuron")
fit_LH <- fastTS(LakeHuron)
fit_LH
#> An endogenous PACF-based fastTS model.
#>
#> PF_gamma AICc_d BIC_d
#> 0.00 4.17 6.56
#> 0.25 3.34 3.54
#> 0.50 2.98 3.22
#> 1.00 1.06 1.24
#> 2.00 *0* *0*
#> 4.00 6.79 2.9
#> 8.00 6.79 2.9
#> 16.00 6.79 2.9
#>
#> AICc_d and BIC_d are the difference from the minimum; *0* is best.
#>
#> - Best AICc model: 4 active terms
#> - Best BIC model: 4 active terms
#>
#> Test-set prediction accuracy (20% held-out test set)
#> rmse rsq mae
#> AICc 0.7751 0.6043019 0.5888855
#> BIC 0.7751 0.6043019 0.5888855
coef(fit_LH)
#> 0.00069
#> (Intercept) 111.8740292
#> lag1 1.1003545
#> lag2 -0.4732437
#> lag3 0.1796316
#> lag4 0.0000000
#> lag5 0.0000000
#> lag6 0.0000000
#> lag7 0.0000000
#> lag8 0.0000000
#> lag9 0.0000000EuStockMarkets
If you have a univariate time series with suspected trend, such as the EuStockMarkets data set,
data("EuStockMarkets")
X <- as.numeric(time(EuStockMarkets))
X_sp <- splines::bs(X-min(X), df = 9)
fit_stock <- fastTS(log(EuStockMarkets[,1]), n_lags_max = 400, X = X_sp, w_exo = "unpenalized")
fit_stock
#> A PACF-based fastTS model with 9 exogenous features.
#>
#> PF_gamma AICc_d BIC_d
#> 0.00 11.36 28.22
#> 0.25 2.18 4.41
#> 0.50 *0* 0.74
#> 1.00 6.46 <0.01
#> 2.00 6.46 *0*
#> 4.00 6.46 <0.01
#> 8.00 6.46 <0.01
#> 16.00 6.46 <0.01
#>
#> AICc_d and BIC_d are the difference from the minimum; *0* is best.
#>
#> - Best AICc model: 18 active terms
#> - Best BIC model: 10 active terms
#>
#> Test-set prediction accuracy (20% held-out test set)
#> rmse rsq mae
#> AICc 0.09071464 0.7328887 0.0758487
#> BIC 0.09292579 0.7197084 0.0780460
tail(coef(fit_stock), 11)
#> 0.0000096
#> lag399 0.000000000
#> lag400 0.000000000
#> 1 0.251818563
#> 2 -0.064008340
#> 3 -0.022147416
#> 4 -0.015421857
#> 5 -0.014734876
#> 6 0.001020223
#> 7 0.011708216
#> 8 0.311147538
#> 9 0.000000000
# insert plot? Seasonal examples
Nottem
data("nottem")
fit_nt <- fastTS(nottem, n_lags_max = 24)
fit_nt
#> An endogenous PACF-based fastTS model.
#>
#> PF_gamma AICc_d BIC_d
#> 0.00 3.86 13.5
#> 0.25 0.43 *0*
#> 0.50 *0* 3.74
#> 1.00 2.49 3.91
#> 2.00 29.29 33.52
#> 4.00 83.31 75.53
#> 8.00 106.95 99.16
#> 16.00 212.75 201.97
#>
#> AICc_d and BIC_d are the difference from the minimum; *0* is best.
#>
#> - Best AICc model: 9 active terms
#> - Best BIC model: 6 active terms
#>
#> Test-set prediction accuracy (20% held-out test set)
#> rmse rsq mae
#> AICc 2.324769 0.9223185 1.747609
#> BIC 2.376213 0.9188426 1.815714
coef(fit_nt)
#> 0.0393
#> (Intercept) 11.89830169
#> lag1 0.40437830
#> lag2 0.00000000
#> lag3 -0.06838188
#> lag4 -0.09660138
#> lag5 -0.01640032
#> lag6 0.00000000
#> lag7 -0.04079986
#> lag8 0.00000000
#> lag9 0.00000000
#> lag10 0.00000000
#> lag11 0.16707390
#> lag12 0.00000000
#> lag13 0.05894906
#> lag14 0.00000000
#> lag15 0.00000000
#> lag16 0.00000000
#> lag17 0.00000000
#> lag18 0.00000000
#> lag19 0.00000000
#> lag20 0.00000000
#> lag21 0.00000000
#> lag22 0.00000000
#> lag23 0.00000000
#> lag24 0.34816025UKDriverDeaths
data("UKDriverDeaths")
fit_ukdd <- fastTS(UKDriverDeaths, n_lags_max = 24)
fit_ukdd
#> An endogenous PACF-based fastTS model.
#>
#> PF_gamma AICc_d BIC_d
#> 0.00 5.97 7.9
#> 0.25 3.91 3.91
#> 0.50 2.25 2.25
#> 1.00 0.77 0.77
#> 2.00 0.02 0.02
#> 4.00 *0* *0*
#> 8.00 10.21 7.55
#> 16.00 39.18 33.83
#>
#> AICc_d and BIC_d are the difference from the minimum; *0* is best.
#>
#> - Best AICc model: 5 active terms
#> - Best BIC model: 5 active terms
#>
#> Test-set prediction accuracy (20% held-out test set)
#> rmse rsq mae
#> AICc 170.9203 0.5776374 131.9969
#> BIC 170.9203 0.5776374 131.9969
coef(fit_ukdd)
#> 0.0282
#> (Intercept) 198.6573213
#> lag1 0.3805100
#> lag2 0.0000000
#> lag3 0.0000000
#> lag4 0.0000000
#> lag5 0.0000000
#> lag6 0.0000000
#> lag7 0.0000000
#> lag8 0.0000000
#> lag9 0.0000000
#> lag10 0.0000000
#> lag11 0.1645141
#> lag12 0.4682378
#> lag13 0.0000000
#> lag14 -0.1357345
#> lag15 0.0000000
#> lag16 0.0000000
#> lag17 0.0000000
#> lag18 0.0000000
#> lag19 0.0000000
#> lag20 0.0000000
#> lag21 0.0000000
#> lag22 0.0000000
#> lag23 0.0000000
#> lag24 0.0000000sunspot
data("sunspot.month")
fit_ssm <- fastTS(sunspot.month)
fit_ssm
#> An endogenous PACF-based fastTS model.
#>
#> PF_gamma AICc_d BIC_d
#> 0.00 24.92 38.93
#> 0.25 7.88 *0*
#> 0.50 *0* 0.48
#> 1.00 69.15 35.7
#> 2.00 221.33 131.01
#> 4.00 434.49 332.77
#> 8.00 434.49 332.77
#> 16.00 434.49 332.77
#>
#> AICc_d and BIC_d are the difference from the minimum; *0* is best.
#>
#> - Best AICc model: 23 active terms
#> - Best BIC model: 14 active terms
#>
#> Test-set prediction accuracy (20% held-out test set)
#> rmse rsq mae
#> AICc 15.94153 0.8920102 11.85384
#> BIC 16.04978 0.8905385 11.99382Model summaries
summary(fit_ssm)
#> Model summary (ncvreg) at optimal AICc (lambda=0.0514; gamma=0.5)
#> lasso-penalized linear regression with n=2224, p=317
#> At lambda=0.0514:
#> -------------------------------------------------
#> Nonzero coefficients : 22
#> Expected nonzero coefficients: 9.57
#> Average mfdr (22 features) : 0.435
#>
#> Estimate z mfdr Selected
#> lag1 0.543429 75.5671 < 1e-04 *
#> lag2 0.100936 14.3108 < 1e-04 *
#> lag9 0.095814 13.9892 < 1e-04 *
#> lag4 0.088981 12.7748 < 1e-04 *
#> lag3 0.077649 11.1365 < 1e-04 *
#> lag6 0.058591 8.7845 < 1e-04 *
#> lag5 0.031138 4.9444 0.00032487 *
#> lag18 -0.028505 -4.4224 0.00358883 *
#> lag102 0.021959 3.7402 0.05826384 *
#> lag27 -0.019987 -3.4042 0.10962497 *
#> lag212 -0.018947 -3.1479 0.18172134 *
#> lag24 -0.018334 -3.0999 0.22925539 *
#> lag111 0.017205 2.9704 0.42075053 *
#> lag92 0.017222 2.8639 0.56575685 *
#> lag12 0.012107 2.3759 1.00000000 *
#> lag20 -0.007329 -1.6906 1.00000000 *
#> lag21 -0.009982 -2.0002 1.00000000 *
#> lag34 -0.004472 -1.3302 1.00000000 *
#> lag55 -0.003429 -1.2274 1.00000000 *
#> lag96 0.001556 1.0625 1.00000000 *
#> lag275 0.000595 0.8962 1.00000000 *
#> lag292 -0.010658 -1.9653 1.00000000 *