No abstract

Many time series encountered in practice are nonstationary, and instead are often generated from a process with a unit root. Because of the process of data collection or the practice of researchers, time series used in analysis and modeling are frequently obtained through temporal aggregation. As a result, the series used in testing for a unit root are often time series aggregates. In this paper, we study the effects of the use of aggregate time series on the Dickey-Fuller test for a unit root. We start by deriving a proper model for the aggregate series. Based on this model, we find the limiting distributions of the test statistics and illustrate how the tests are affected by the use of aggregate time series. The results show that those distributions shift to the right and that this effect increases with the order of aggregation, causing a strong impact both on the empirical significance level and on the power of the test. To correct this problem, we present tables of critical points appropriate for the tests based on aggregate time series and demonstrate their adequacy. Examples illustrate the conclusions of our analysis.

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With the benefits of increased computing power and much improved software, temporal disaggregation is examined. Disaggregation, the process of obtaining high frequency data from low frequency data has been discussed for many years. This study examines three methods which utilize the autoregressive integrated moving average (ARIMA) model in a simulation study comparing parameter estimation, disaggregation mean square error, and forecast mean square error. Finally, the three methods are applied to a real-world time series.

We considered building high performance tools on the Raspberry Pi 4. We implemented OpenMP and OpenCoarrays Fortran in conjunction with the statistical language R. We found that the OpenCoarrays is more effective when working with vectors, while OpenMP is better in the arena with large matrices in a geostatistics application. These results can be very useful for researchers with limited access to high performance tools or limited funding.