Essay on Comparing STLF & Snaive Forecasts: Clay Brick Production in Australia (1956-1994)

This paper is reconstructed of a time series forecast, which tends to compare forecasts from self with those from naive, using a test set comparing the last two years of data. In this regard, a comparison will be made to establish which forecast is better. Additionally, the paper will try to find out the error which is likely to occur when creating the forecast. The forecast comprised of bricks data specifically on the Australian quarterly clay brick production raging from 1956-1994. The STL decomposition method was applied to calculate the trend-cycle and seasonal indices. The experiment could have either fixed or changed seasonality. Computation of the seasonally adjusted data was done and later plotting was done. The use of self to personalise the results was done, giving the forecast for the original data. Additionally, the results were used to determine whether the residue looked uncorrelated or not. Later a repeat of the same was done using the robust STL decomposition method to establish whether there was a notable difference in the results.

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STL is a versatile and robust method that is used for decomposing time series. Furthermore, STL is an acronym used for Seasonal and Trend decomposition using Loess (Theodosiou, 2011). On the other hand, Loess is a method that is used to estimate nonlinear relationships. The STL method was used to find out the trend cycle and seasonal indices. In this question, a plotting of the trend-cycle and seasonal indices was done. The data was computed by the multiplicative decomposition functions, indicating an upward trend.

Additionally, the results indicate that there is a seasonal fluctuation as well as fairly random residuals. The naïve method was used in the forecasting process. The naïve method is a technique in which the last period's actuals are used as this period's forecast (Sezen, Unal & Deniz, 2020). In this regard, without adjusting periods or attempting to establish causal factors. This method is used in making a comparison with the forecasts generated in better ways. Using the naïve approach, forecasts are produced that are equal to the last observed value. The graph drawn using the naïve method shows a new order index against time between 1960 to 1990. The graph is a naïve forecast of seasonally adjusted data.

STLF was used to personalise the results, which helped to give original data. From the earlier definition, STLF is a seasonal and Trend decomposition using the Loess Forecast model. A complete procedure concerning the STLF method can be divided into decomposition and forecasting. In this case, one method can pave the way for the other. The STLF method combines the stlm and forecast methods. The stlf takes a ts argument, models the seasonally adjusted data, applies an STL decomposition, seasonalizes, and finally returns the forecasts. Furthermore, it is possible to specify the time series models for the seasonally adjusted data in the STLM by applying either method or model function. The results were obtained by ft stlf <- stlf (bricksq, method= naïve) forecast (ft stlf, h =8). The results were generated for a specific timeline between 1994-1996. For instance, the point forecast for 1994 Q4 was registered as 465.7338, while 1996 Q3 registered 494.000. The entire forecast represented eight outcomes (h=8).

A forecast was done to determine whether the residuals are correlated or uncorrelated. It implies that if there is a correlation between the residuals, then there is information left in the residuals which needs to be used in the computation forecast. Additionally, the residuals should have a zero mean. When the residuals have a different mean other than zero, it implies that the forecasts are biased. In this case, there is a warning in the check residuals (ft stlf). The fitted degrees of freedom are based on the model used for seasonally adjusted data. Data residuals from the STL + Random walk were used where Q* = 40.829, df =8, p-value = 2.244e-06. The total lags used is eight at the quarter of 4 and 8. In this case, there is a slight correlation. However, this notable correlation is acceptable for a naïve forecast.

The forecast was done again with a robust STL decomposition method to determine whether there is a difference in the results. In doing so, plotting was done on new orders index against time for the naïve forecasts of seasonally adjusted data. Forecast (ft-st12, h=8) was done between 1994-1996. For example, the point forecast for 1994 Q4 was 470.9904, while 1996 Q3 was 493.6721. This indicates that there is a slight difference in the forecast results. However, robustness does not significantly influence the results. A comparison can be made to determine between self and naive, which one is better. In doing so, a test set comprising the last two years of data was used. From the graph drawn on bricks against time between 1990 and 1994, the original data curve is above the stlf and snaive curves. However, both self and snaive curves lie cross to each other. From the results obtained, stlf method is better compared to the snaive method since it provides more accurate data.

References

Sezen, I., Unal, A., & Deniz, A. (2020). Anomaly detection by STL decomposition and extended isolation forest on environmental univariate time series. https://doi.org/10.5194/egusphere-egu2020-18471

Theodosiou, M. (2011). Forecasting monthly and quarterly time series using STL decomposition. International Journal of Forecasting, 27(4), 1178-1195. https://doi.org/10.1016/j.ijforecast.2010.11.002