2 Trend _ Time series analysis

The mean function of a general time series is a completely arbitrary time function, and the mean function of stationary time series is a constant in a certain time domain. 1 Deterministic trends and stochastic trends

An estimate of the 2 constant mean value of the modeling method for determining trends is given below

Assuming that the mean function is constant, the model can be written as
Y T =μ+x t
where all t have E (X t) =0
If the time series Y 1, y 2,..., y n is used to estimate μ, the most common is that the estimation of μ is a sample mean or an average.
For stationary sequences, the variance of the mean estimator is generally inversely proportional to the sample size.
For non-stationary sequences (but with constant mean value), the variance of mean estimator is generally increased with the increase of sample size.
It is obvious that for non-stationary sequences, it is not possible to estimate the sample mean, and other methods should be considered. 3 Regression method

Traditional regression analysis and statistical methods can easily estimate the parameters of the general mean trend model of extraordinary numbers. This paper mainly introduces linear trend, two times trend, seasonal mean trend and cosine trend. 1 linear trend of time and two times trend

Consider the following trends in determining time:
μt =β0 +β1 T
The most common choice least squares estimation parameter value 2 cyclical or seasonal trend 3 strings trend 4 regression estimate reliability and effectiveness 5 regression results Interpretation 6 residual analysis