Fits an ARIMA model with exogenous regressors (ARIMAX).
Usage
ts_arimax(
x,
xreg,
order = NULL,
seasonal = NULL,
stepwise = TRUE,
approximation = TRUE,
...
)Arguments
- x
A complete
ts_dfwith no missing values.- xreg
A matrix or data.frame of exogenous regressors with
nrow(xreg) == nrow(x).- order
Optional non-seasonal ARIMA order. If
NULL(default), automatic order selection viaforecast::auto.arima().- seasonal
Optional seasonal specification.
- stepwise, approximation
Passed to
forecast::auto.arima().- ...
Additional arguments passed to the forecast fitting function.
Value
A list containing tidy model summaries, the raw model, input, and the exogenous regressors used.
Examples
x = as_ts_df(log(AirPassengers))
xreg = data.frame(trend = seq_len(nrow(x)))
ts_arimax(x, xreg = xreg)
#> $model_info
#> # A tibble: 1 × 5
#> log_lik aic aicc bic sigma2
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 212. -407. -406. -383. 0.00289
#>
#> $coefficients
#> # A tibble: 7 × 3
#> term estimate std_error
#> <chr> <dbl> <dbl>
#> 1 ma1 0.738 0.0835
#> 2 ma2 0.596 0.0986
#> 3 ma3 0.243 0.0823
#> 4 sma1 0.828 0.0826
#> 5 sma2 0.650 0.103
#> 6 intercept 4.82 0.0469
#> 7 trend 0.00992 0.000544
#>
#> $fitted
#> # A tibble: 144 × 4
#> time observed fitted residual
#> <int> <dbl> <dbl> <dbl>
#> 1 1 4.72 4.77 -0.0540
#> 2 2 4.77 4.77 0.00443
#> 3 3 4.88 4.83 0.0491
#> 4 4 4.86 4.89 -0.0285
#> 5 5 4.80 4.85 -0.0574
#> 6 6 4.91 4.84 0.0664
#> 7 7 5.00 4.93 0.0669
#> 8 8 5.00 5.00 -0.00652
#> 9 9 4.91 4.96 -0.0475
#> 10 10 4.78 4.85 -0.0671
#> # ℹ 134 more rows
#>
#> $diagnostics
#> # A tibble: 1 × 5
#> test lag statistic p_value conclusion
#> <chr> <int> <dbl> <dbl> <chr>
#> 1 Ljung-Box 13 50.9 0 Autocorrelation detected
#>
#> $model
#> Series: x_ts
#> Regression with ARIMA(0,0,3)(0,0,2)[12] errors
#>
#> Coefficients:
#> ma1 ma2 ma3 sma1 sma2 intercept trend
#> 0.7384 0.5956 0.2430 0.8282 0.6496 4.8183 0.0099
#> s.e. 0.0835 0.0986 0.0823 0.0826 0.1027 0.0469 0.0005
#>
#> sigma^2 = 0.002887: log likelihood = 211.57
#> AIC=-407.14 AICc=-406.08 BIC=-383.39
#>
#> $input
#> time value
#> 1 1 4.718499
#> 2 2 4.770685
#> 3 3 4.882802
#> 4 4 4.859812
#> 5 5 4.795791
#> 6 6 4.905275
#> 7 7 4.997212
#> 8 8 4.997212
#> 9 9 4.912655
#> 10 10 4.779123
#> 11 11 4.644391
#> 12 12 4.770685
#> 13 13 4.744932
#> 14 14 4.836282
#> 15 15 4.948760
#> 16 16 4.905275
#> 17 17 4.828314
#> 18 18 5.003946
#> 19 19 5.135798
#> 20 20 5.135798
#> 21 21 5.062595
#> 22 22 4.890349
#> 23 23 4.736198
#> 24 24 4.941642
#> 25 25 4.976734
#> 26 26 5.010635
#> 27 27 5.181784
#> 28 28 5.093750
#> 29 29 5.147494
#> 30 30 5.181784
#> 31 31 5.293305
#> 32 32 5.293305
#> 33 33 5.214936
#> 34 34 5.087596
#> 35 35 4.983607
#> 36 36 5.111988
#> 37 37 5.141664
#> 38 38 5.192957
#> 39 39 5.262690
#> 40 40 5.198497
#> 41 41 5.209486
#> 42 42 5.384495
#> 43 43 5.438079
#> 44 44 5.488938
#> 45 45 5.342334
#> 46 46 5.252273
#> 47 47 5.147494
#> 48 48 5.267858
#> 49 49 5.278115
#> 50 50 5.278115
#> 51 51 5.463832
#> 52 52 5.459586
#> 53 53 5.433722
#> 54 54 5.493061
#> 55 55 5.575949
#> 56 56 5.605802
#> 57 57 5.468060
#> 58 58 5.351858
#> 59 59 5.192957
#> 60 60 5.303305
#> 61 61 5.318120
#> 62 62 5.236442
#> 63 63 5.459586
#> 64 64 5.424950
#> 65 65 5.455321
#> 66 66 5.575949
#> 67 67 5.710427
#> 68 68 5.680173
#> 69 69 5.556828
#> 70 70 5.433722
#> 71 71 5.313206
#> 72 72 5.433722
#> 73 73 5.488938
#> 74 74 5.451038
#> 75 75 5.587249
#> 76 76 5.594711
#> 77 77 5.598422
#> 78 78 5.752573
#> 79 79 5.897154
#> 80 80 5.849325
#> 81 81 5.743003
#> 82 82 5.613128
#> 83 83 5.468060
#> 84 84 5.627621
#> 85 85 5.648974
#> 86 86 5.624018
#> 87 87 5.758902
#> 88 88 5.746203
#> 89 89 5.762051
#> 90 90 5.924256
#> 91 91 6.023448
#> 92 92 6.003887
#> 93 93 5.872118
#> 94 94 5.723585
#> 95 95 5.602119
#> 96 96 5.723585
#> 97 97 5.752573
#> 98 98 5.707110
#> 99 99 5.874931
#> 100 100 5.852202
#> 101 101 5.872118
#> 102 102 6.045005
#> 103 103 6.142037
#> 104 104 6.146329
#> 105 105 6.001415
#> 106 106 5.849325
#> 107 107 5.720312
#> 108 108 5.817111
#> 109 109 5.828946
#> 110 110 5.762051
#> 111 111 5.891644
#> 112 112 5.852202
#> 113 113 5.894403
#> 114 114 6.075346
#> 115 115 6.196444
#> 116 116 6.224558
#> 117 117 6.001415
#> 118 118 5.883322
#> 119 119 5.736572
#> 120 120 5.820083
#> 121 121 5.886104
#> 122 122 5.834811
#> 123 123 6.006353
#> 124 124 5.981414
#> 125 125 6.040255
#> 126 126 6.156979
#> 127 127 6.306275
#> 128 128 6.326149
#> 129 129 6.137727
#> 130 130 6.008813
#> 131 131 5.891644
#> 132 132 6.003887
#> 133 133 6.033086
#> 134 134 5.968708
#> 135 135 6.037871
#> 136 136 6.133398
#> 137 137 6.156979
#> 138 138 6.282267
#> 139 139 6.432940
#> 140 140 6.406880
#> 141 141 6.230481
#> 142 142 6.133398
#> 143 143 5.966147
#> 144 144 6.068426
#>
#> $xreg
#> trend
#> [1,] 1
#> [2,] 2
#> [3,] 3
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#>