library(srlTS)
library(magrittr) # for pipedata("LakeHuron")
fit_LH <- srlTS(LakeHuron)
fit_LH
#> PF_gamma best_AICc best_BIC
#> 0.00 147.2053 159.8118
#> 0.25 146.3811 156.7937
#> 0.50 146.0177 156.4739
#> 1.00 144.1002 154.4967
#> 2.00 143.0362 153.2544
#> 4.00 149.8227 156.1558
#> 8.00 149.8227 156.1558
#> 16.00 149.8227 156.1558
#>
#> Test-set prediction accuracy
#> rmse rsq mae
#> AIC 0.7751 0.6203825 0.5888855
#> BIC 0.7751 0.6203825 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 0.0000000If 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 <- srlTS(log(EuStockMarkets[,1]), n_lags_max = 400, X = X_sp, w_exo = "unpenalized")
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? data("nottem")
fit_nt <- srlTS(nottem, n_lags_max = 24)
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 0.34816025data("UKDriverDeaths")
fit_ukdd <- srlTS(UKDriverDeaths, n_lags_max = 24)
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 0.0000000Adding holiday indicators…
data("sunspot.month")
fit_ssm <- srlTS(sunspot.month)
fit_ssm
#> PF_gamma best_AICc best_BIC
#> 0.00 18373.20 18506.04
#> 0.25 18356.15 18467.11
#> 0.50 18348.28 18467.59
#> 1.00 18417.42 18502.81
#> 2.00 18569.61 18598.12
#> 4.00 18782.77 18799.88
#> 8.00 18782.77 18799.88
#> 16.00 18782.77 18799.88
#>
#> Test-set prediction accuracy
#> rmse rsq mae
#> AIC 15.94153 0.8920872 11.85384
#> BIC 16.04978 0.8906613 11.99382Model summaries
summary(fit_ssm)
#> Model summary 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: 11.05
#> Average mfdr (22 features) : 0.502
#>
#> 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 0.001529 *
#> lag18 -0.028505 -4.4224 0.014416 *
#> lag102 0.021959 3.7402 0.166810 *
#> lag27 -0.019987 -3.4042 0.387958 *
#> lag212 -0.018947 -3.1479 0.588979 *
#> lag24 -0.018334 -3.0999 0.623896 *
#> lag111 0.017205 2.9704 0.709145 *
#> lag92 0.017222 2.8639 0.767884 *
#> lag12 0.012107 2.3759 0.921349 *
#> lag21 -0.009982 -2.0002 0.963700 *
#> lag292 -0.010658 -1.9653 0.966033 *
#> lag20 -0.007329 -1.6906 0.979140 *
#> lag34 -0.004472 -1.3302 0.987783 *
#> lag55 -0.003429 -1.2274 0.989271 *
#> lag96 0.001556 1.0625 0.991100 *
#> lag275 0.000595 0.8962 0.992427 *