This paper derives the exact distribution of the maximum likelihood estimator of a first order linear autoregression with exponential innovations. We show that even if the process is stationary, the estimator is $T$-consistent, where $T$ is the sample size. In the unit root case the estimator is...

A new two-way map between time domain and numerical magnitudes or values domain (v-dom) provides a new solution to heteroscedasticity. Since sorted logs of squared fitted residuals are monotonic in the v-dom, we obtain a parsimonious fit there. Two theorems prove consistency, asymptotic...

Using component series from a given time series, we are able to demonstrate forecasting ability with none of the requirements of the traditional ARMA method, while strictly adhering to the definition of an autoregressive model. We also propose a new test for seasonality using coefficient of...