Table 2 Methods Summary

Edwards’ Test [12,13,14]

ED

Hypothesis test of a harmonic model of data using a linear combination of sine and cosine (periodic for 2nπ, thus trend removal is not required). The modeled data are fit using a Poisson generalized linear model. Seasonality is determined by evaluating the peaks and troughs of the modeled curve fit to the observed time series. Implementation in R follows [14].

Friedman’s Test [15]

FR

Hypothesis test using a non-parametric approach for comparing samples within a population or from populations with identical medians. A rank-based approach is employed to test the hypothesis of no seasonality of the ranked months. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [11].

ARIMA Hypothesis Test [9, 16,17,18,19,20]

AR

Hypothesis test to determine if the seasonal component is significant when compared to an identical ARIMA model without a seasonal component. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [9].

QS Test [21]

QS

Hypothesis test to determine seasonality by examining the autocorrelation of seasonal lags. The observed time series is seasonal if positive autocorrelations at either lag 12 or 24 are significant. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [11].

ETS Hypothesis Test [9, 16,17,18,19,20]

ET

Hypothesis test to determine if the seasonal component is significant when compared to an identical ETS model without a seasonal component. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [9].

Kruskal-Wallis Test [22]

KW

Hypothesis test using a non-parametric approach to compare samples from a population. A rank-based approach is employed to test the hypothesis that the monthly data have the same mean. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [11].

Welch’s Test [23]

WE

Hypothesis test employing one-way ANOVA, but allowing for unequal variances amongst the groups of months. Seasonality is determined if hypothesis that the monthly means are identical is rejected. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [11].

Auto ARIMA Test [9, 16,17,18,19,20]

AA

Test based on minimizing forecast errors across different models. The observed time series is considered seasonal if the optimal ARIMA model chosen (the one that minimizes forecast error) includes a seasonal component. Any linear trend in the data is removed prior to testing for seasonality. Implementation in R follows [9].