Time Series Analysis in Forecasting Mental Addition and Summation Performance

An ideal performance evaluation metric would be predictive, objective, easy to administer, estimate the variance in performance, and provide a confidence interval for the level of uncertainty. Time series forecasting may provide objective metrics for predictive performance in mental arithmetic. Addition and summation (addition combined with subtraction) using the Japanese Soroban computation system was undertaken over 60 days. The median calculation time in seconds for adding 10 sequential six digit numbers [CT(Add)) was 63 s (interquartile range (IQR) = 12, range 48–127 s], while that for summation (CT(Sum)) was 70 s (IQR = 14, range 53–108 s), and the difference between these times was statistically significant p < 0.0001. Using the mean absolute percentage error (MAPE) to measure forecast accuracy, the autoregressive integrated moving average (ARIMA) model predicted a further reduction in both CT(Add) to a mean of 51.51 ± 13.21 s (AIC = 5403.13) with an error of 6.32%, and CT(Sum) to a mean of 54.57 ± 15.37 s (AIC = 3852.61) with an error of 8.02% over an additional 100 forecasted trials. When the testing was repeated, the actual mean performance differed by 1.35 and 4.41 s for each of the tasks, respectively, from the ARIMA point forecast value. There was no difference between the ARIMA model and actual performance values (p-value CT(Add) = 1.0, CT(Sum)=0.054). This is in contrast to both Wright's model and linear regression (p-value < 0.0001). By accounting for both variability in performance over time and task difficulty, forecasting mental arithmetic performance may be possible using an ARIMA model, with an accuracy exceeding that of both Wright's model and univariate linear regression.