You might look at the correlations between pairs of data (i.e. two time series). High correlation would indicate that the variation in one variable explains the variation in the other. It could either point at a cause-effect relationship or that the variation in both is affected by a common cause.

You must bear in mind that there is no way you can predict one time series with an accuracy level of 100 percent. There is always a degree of uncertainty. The higher the correlation coefficient (absolute value close to 1) the greater the level of accuracy in the prediction based on the input time series.

There are other variables that will affect your forecasts that are unaccounted for in your model. For instance, mean temperature can be affected by the type of surface, cloud cover and whether there is precipitation. To illustrate the case, in California, because of the forest fires, the smoke had the effect of lowering visibility even in downwind locations over 100 km away from the fires. The smoke cloud also reduced the amount of sunlight reaching the ground and consequently the air temperature was lower than in normal days in those downwind locations although at locations closer to the fires the temperature was obviously higher due to their proximity to the source of heat.

Hi, you can also use Mean Squared Prediction Error.

In addition you can try to carry out inference, I mean hypothesis testing to explore if the differences your are detecting between two MSPE or two MAPE are statistically significant or not. Check the famous Diebold and Mariano (1995) test.

You can also test for forecast efficiency: are your forecasts biased? are your forecast erros correlated with your forecasts? An efficient forecast should have forecast errors that are zero mean and unrelated to variables available at the time the forecast was made.

Hope it helps!

Mean Absolute Percentage Error should not be used for temperatures (in Celsius degrees, I suppose) since it requires strictly positive data. There have been questions on RG about comparing time series. I would not compare a series of data with a series of forecasts. Good luck.

Please let me recommend this framework for forecast evaluation:

Conference Paper Data Formats and Visual Tools for Forecast Evaluation in Cyb...

Hopefully, the above framework is powerful enough to meet your research needs.

Major features:

1) supports many methods, horizons, origins, and series

2) gives direct instructions on what metrics to use and how

3) gives exact data formats to keep and update your actuals and forecasts as new data becomes available

If you should have questions, please let me know. Some elements the framework are under development, so we're interested in obtaining some feedback from practitioners.

P.S. Agree with Guy Mélard - MAPEs are not recommended. We recommend the AvgRelMAE, as can be seen on the above slide 23:

Conference Paper Data Formats and Visual Tools for Forecast Evaluation in Cyb...