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The slope of an equation is proportional to the correlation coefficient multiplied by the ratio of the two standard deviations (sigmay/sigmax) . Since x is y lag 1 the ratio is nearly unity thus the r …

Yes .... If you have yt=XtB+ut where ut=ρut−1+et, et is iid and you clear fractions then you have a model of the form y(t)= γy(t−1) + X_{t}-[1-γ]X_{t-1} + e_t$, and $e_t$ is iid. where $w_t= …

Think of the ACF as unconditional auto-regression coefficients reflecting the importance of any 1 AND ONLY 1 particular lag. Now think of the PACF as a set of conditional auto-regression coefficients …

For each time series estimate an AR(2) model for all the 1000 values and then for different subsets e.g. 1-100 and 101-1000 ( break point 101) and perform a CHOW test for constancy of parameters (1960 …

For non-seasonal data if the ACF is dominant then the order of the AR model is the last significant PACF value ...reverse this logic to asses the order of the MA model If you tons of significant ACF a …

Just saw your question ... Please look at how to generate random time series for a given one, including all trends? for my suggestion as to how to simulate a series given its DGF ( read model form ! ) …

this acf suggests non-stationarity which might be remedied by incorporating a daily effect as it appears to evidence structure at lag 24. The daily effect could be either auto-regressive of order 24 o …

The DW statistic tests whethwer or not there is first order autocorrelation in the residuals. … It ignores a host of other possible violations likw autocorrelation of lag 12 or any other lag in the errors. …

Use daily data to develop a useful model. You can then accumulate the forecasts into weekly or monthly buckets as you wish. The daily model could contain structure like day-of-the-week ,day-of-the-mon …

why take logs why difference by unnecessarily differencing you can inject structure into the residuals. did you take into account that the seasonality might be deterministic ? did you identify an …

By summing the series to an annual level you remove the seasonal autocorrelation and the period to period autocorrelation. … The autocorrelation of the annual series may still exist depending on the data. …

Auto-correlation in the residuals can be masked/suppressed by Pulses/Seasonal Pulses or the resultant of omitted Level/Step shifts or Local Time Trends. Auto-correlation in the residuals may be the re …

Your first series seems uncorrelated whole your second series looks like an Ar(1). The Q statistics you are computing are incorrectly suggesting structure. The reason is you have a ton (3665) of obser …

Yes that is correct auto-correlation is a sequence of correlations taken at fixed intervals. If the auto-correlation decays while the partial correlation (conditional correlation ) cuts off after k va …

If you construct a regression model (perhaps with additional arima structure thus ARMAX ) using 6 dummies to reflect day-of-the-week and 51 dummies reflecting week of the year you might accomplish wha …