# There invented by the mathematicians Karl Friedrich

There are several economists have worked on the issue of explaining natural gas demand in recent years, including economic indicators in their models and using various estimation techniques. Forouzanfar et al. (2010) and Toksar (2010), at the request of Iran and Turkey, respectively, are developing models to predict the demand for natural gas by using economic and scientific variables 29.Time series models can be configured as univariate or multivariate models. In a univariate specification called the Autoregressive Integrated Moving Average (ARIMA), the future estimates of a variable are based on the same variables. The ARIMA specification takes the following general forms: yt = a0 + a1yt?1 + …

+ apyt?p + ?t + b1?t?1 + …

+ bq?t?q. (1) In most cases, in addition to the delays of the dependent variable, it is useful to include in the specification the independent factors that are thought to influence the dependent variable. As this study predicts natural gas consumption, basically to include other independent variables such as temperature, gross domestic product change (% ).Formally, an ARMA model can be expressed as a structural equation and an equation to specify disturbances 30. yt = Xt? + ?t, (2) The regression of the linear least squares is named as the estimates of the unknown parameters are calculated. In the late 1700’s and the early 1800’s the “method of least squares” that is used to obtain parameter estimates was independently invented by the mathematicians Karl Friedrich Gauss, Adrien Marie Legendre and (possibly) Robert Adrain Stigler (1978) Harter (1983) Stigler (1986) working in Germany, France and America, respectively. In the method of least squares, unknown parameters are estimated by reducing the sum of the squares in the squares between the data and the model to the smallest.

The minimization process reduces the over-determined system of equations generated by the data and the equilibrium of a reasonable p system in the unknown system (where p is the number of parameters in the functional section). This new system of equations is then solved to obtain parameter estimates.