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The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference. [ 12 ] [ 13 ] ARMA models were popularized by a 1970 book by George E. P. Box and Jenkins, who expounded an iterative ( Box–Jenkins ) method for choosing and estimating them.
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...
Statistical assumptions can be put into two classes, depending upon which approach to inference is used. Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5]
Standard linear regression models with standard estimation techniques make a number of assumptions about the predictor variables, the response variable and their relationship. Numerous extensions have been developed that allow each of these assumptions to be relaxed (i.e. reduced to a weaker form), and in some cases eliminated entirely.
The first statistical assumption constitutes a statistical model: because with the assumption alone, we can calculate the probability of any event. The alternative statistical assumption does not constitute a statistical model: because with the assumption alone, we cannot calculate the probability of every event. In the example above, with the ...
The order p and q can be determined using the sample autocorrelation function (ACF), partial autocorrelation function (PACF), and/or extended autocorrelation function (EACF) method. [ 10 ] Other alternative methods include AIC, BIC, etc. [ 10 ] To determine the order of a non-seasonal ARIMA model, a useful criterion is the Akaike information ...
The assumptions underlying a t-test in the simplest form above are that: X follows a normal distribution with mean μ and variance σ 2 /n. s 2 (n − 1)/σ 2 follows a χ 2 distribution with n − 1 degrees of freedom. This assumption is met when the observations used for estimating s 2 come from a normal distribution (and i.i.d. for each group).
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
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