TBATS Time Series Modelling in R
TBATS Time Series Modelling in R, The term “TBATS” refers to a well-liked time series forecasting technique and stands for
- Trigonometric seasonality
- Box-Cox transformation
- ARMA errors
- Trend
- Seasonal components
The following models can be used with and without this method
- Seasonality
- A Box-Cox transformation
- ARMA(p, q) process
- Various trends
- Various seasonal effects
The final model in this procedure will be the one with the lowest Akaike Information Criterion (AIC) score.
Using the tbats function from the forecast package is the simplest way to fit a TBATS model to a time series dataset in R.
How to actually use this function is demonstrated in the example that follows.
How to Fit a TBATS Time Series Modelling in R
We’ll use USAccDeaths, a built-in R dataset that contains values for the total monthly accidental fatalities in the USA from 1973 to 1978, for this example.
Now we can view the USAccDeaths dataset
USAccDeaths
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1973 9007 8106 8928 9137 10017 10826 11317 10744 9713 9938 9161 8927 1974 7750 6981 8038 8422 8714 9512 10120 9823 8743 9129 8710 8680 1975 8162 7306 8124 7870 9387 9556 10093 9620 8285 8466 8160 8034 1976 7717 7461 7767 7925 8623 8945 10078 9179 8037 8488 7874 8647 1977 7792 6957 7726 8106 8890 9299 10625 9302 8314 8850 8265 8796 1978 7836 6892 7791 8192 9115 9434 10484 9827 9110 9070 8633 9240
To fit a TBATS model to this dataset and forecast the values of upcoming months, use the following code.
library(forecast)
Yes, now we can fit the TBATS model
TBATSfit <- tbats(USAccDeaths)
Let’s use the model to make the predictions
predict <- predict(TBATSfit)
We can view the predictions
predict
Point Forecast Lo 80 Hi 80 Lo 95 Hi 95 Jan 1979 8307.597 7982.943 8632.251 7811.081 8804.113 Feb 1979 7533.680 7165.539 7901.822 6970.656 8096.704 Mar 1979 8305.196 7882.740 8727.651 7659.106 8951.286 Apr 1979 8616.921 8150.753 9083.089 7903.978 9329.864 May 1979 9430.088 8924.028 9936.147 8656.137 10204.038 Jun 1979 9946.448 9403.364 10489.532 9115.873 10777.023 Jul 1979 10744.690 10167.936 11321.445 9862.621 11626.760 Aug 1979 10108.781 9499.282 10718.280 9176.632 11040.929 Sep 1979 9034.784 8395.710 9673.857 8057.405 10012.162 Oct 1979 9336.862 8668.087 10005.636 8314.060 10359.664 Nov 1979 8819.681 8124.604 9514.759 7756.652 9882.711 Dec 1979 9099.344 8376.864 9821.824 7994.407 10204.282 Jan 1980 8307.597 7563.245 9051.950 7169.208 9445.986 Feb 1980 7533.680 6769.358 8298.002 6364.750 8702.610 Mar 1980 8305.196 7513.281 9097.111 7094.067 9516.325 Apr 1980 8616.921 7800.849 9432.993 7368.847 9864.995 May 1980 9430.088 8590.590 10269.585 8146.187 10713.988 Jun 1980 9946.448 9084.125 10808.771 8627.639 11265.257 Jul 1980 10744.690 9860.776 11628.605 9392.859 12096.522 Aug 1980 10108.781 9203.160 11014.402 8723.753 11493.809 Sep 1980 9034.784 8109.000 9960.567 7618.920 10450.647 Oct 1980 9336.862 8390.331 10283.392 7889.269 10784.455 Nov 1980 8819.681 7854.387 9784.976 7343.391 10295.972 Dec 1980 9099.344 8114.135 10084.554 7592.597 10606.092
The predicted death toll for the following months is displayed along with the confidence ranges of 80% and 95%.
For instance, the forecasts are as follows for January 1979:
Deaths are expected to total 8,307.597.
[7,982.943, 8,632.251] is the 80 percent confidence interval for the number of fatalities ]
A 95 percent [7,811.081, 8,804.113] is the confidence interval for the number of deaths]
We can also plot these anticipated future values using the plot() function:
Now we can plot the predicted values
plot(forecast(TBATSfit))
Future anticipated values are represented by the blue line, while the confidence interval bounds are shown by the grey bands.
