Case Studies

If you're interested in time series analysis and forecasting, this is the right place to be. The Time Series Lab (TSL) software platform makes time series analysis available to anyone with a basic knowledge of statistics. Future versions will remove the need for a basic knowledge altogether by providing fully automated forecasting systems. The platform is designed and developed in a way such that results can be obtained quickly and verified easily. At the same time, many advanced time series and forecasting operations are available for the experts. In our case studies, we often present screenshots of the program so that you can easily replicate results.

Did you know you can make a screenshot of a TSL program window? Press Ctrl + p to open a window which allows you to save a screenshot of the program. The TSL window should be located on your main monitor.

Click on the buttons below to go to our case studies. At the beginning of each case study, the required TSL package is mentioned. Our first case study, about the Nile data, is meant to illustrate the basic workings of the program and we advise you to start with that one.

Sea and land temperature

Author: Rutger Lit
Date: July 05, 2022
Software: Time Series Lab - Home Edition
Topics: Integrated Random Walk
Batch program: temperature.txt

Smooth trend

The data for this case study is the HadCRUT5 annual data on global sea and land temperature. HadCRUT is a dataset of monthly instrumental temperature records formed by combining the sea surface temperature records compiled by the Hadley Centre of the UK Met Office and the land surface air temperature records compiled by the Climatic Research Unit (CRU) of the University of East Anglia. The time series are presented as temperature anomalies (deg C) relative to 1961-1990. The data can be found here.
The data can also be found in the data folder located in the install folder of TSL under the name global temp.csv. Loading and plotting the data in TSL shows an upward trend in the data starting in the 1980's so we clearly need a slope component in our model. Furthermore, the autocorrelation function shows clear signs of long memory.

Integrated Random Walk

Select a time-varying level and time-varying slope on the Build your own model page. Go to the Estimation page and set the end of the Training sample to 141 (1990-01-01). Estimate the model and when TSL is done, go to the Forecast page. Under Plot options set the forecast to 32 periods ahead and select multi-step-ahead forecast. Verify that the multi-step-ahead forecasts are bad. So how to improve?
Go to the Build your own model page and select a fixed level and time-varying slope. The corresponding model is called an Integrated Random Walk model and the result is a model with a much smoother trend. Estimate the model and go to the Forecast page. Verify that the multi-step-ahead forecasts are already much better and all, except two, data points lie within ± 1 standard error. Going back to the Graph page and plotting the ACF for the Predicted residuals reveals first-lag autocorrelation.
Add an ARMA(1,0) component to our latest model and estimate the model. The result is an increase in log likelihood, no significant autocorrelation in the Predicted residuals and an even better forecasting performance. The training sample results, test sample results, and the Forecasting performance are shown in the following figures.

Temperature data with Integrated Random Walk

Data inspection and preparation page

32-step-ahead forecast for Temperature data

Data inspection and preparation page

Forecasting performance for three models

Data inspection and preparation page