STATISTICAL ANALYSIS

Statistical Analysis

Statistical Analysis

Introduction

Global or portmanteau contrasts for FAS series of estimated residuals. Prediction with ARIMA model estimated in SPSS. Criteria ARIMA model selection in SPSS for a series of data (standard error, logarithm statistical likelihood function and Akaike and BIC). 7. Analysis of the distribution of the estimated residuals exploratory analysis of the waste (summary statistics, histograms, outliers, etc.).

Discussion

Part (ar) mean autoregressive (autoregressive) and part (ma) means the moving average (moving average) and this means that the model combines two approaches to estimate a regression approach and the methodology of self-moving averages. This model is called model-Box - Jenkins, the proportion of Mkchwih and is used mainly to predict the value of the string in the short term. And is characterized by this type of forecasting models that totally ignores the impact of explanatory variables, but adopt the prediction values ??of the dependent variable in the future using this model to current and past values ??of the variables.

The second operation or the second approach in the form of a moving average (moving averages) and symbolized by (ma) and here expressed as a function of the dependent variable values ??in the past reduce the random line, which they can gain access to the moving averages for the previous values ??of the variable.

Autoregressive integrated moving average (autoregressive integrated moving average, ARIMA) model is a generalization of autoregressive moving average . These models are used when working with time series for a better understanding of the data or the prediction of future points of the series. Typically, the model is referred to as ARIMA (p, d, q), where p, d and q - non-negative integers characterizing the order for the parts of the model (respectively, autoregressive, integrated and moving average).

ARIMA (p, d, q) obtained by integrating the ARMA (p, q).

where d - a positive integer specifying the level of differentiation (if d = 0, this model is equivalent to autoregressive moving average). Conversely, applying the term by term derivation d times to ARMA (p, q), we obtain the model ARIMA (p, d, q). Note that it is only necessary to differentiate the autoregressive part.

It is important to note that not all combinations of parameters give a "good" model. In particular, to obtain a stationary model requires the fulfillment of certain conditions.

There are several known special cases of model ARIMA. For example, ARIMA (0,1,0), giving the is a model of random walks .

Then we arrive at a model VARIMA. Sometimes a model may be a seasonal factor. An example is a model volume of traffic during the day. At the weekend a number of behavior will be noticeably different from working days. In this case, instead of build orders moving average and autoregressive part of the model, it is better to resort to a model of the seasonal autoregressive moving average (SARIMA). If there is a long-term dependence, the parameter d can be replaced with non-integer values, resulting in drobnointegrirovannomu autoregressive moving average process (FARIMA or ARFIMA).

ARIMA models try to express the evolution of a variable Yt of a stochastic process based on the past of that random variable or that variable impacts suffered in the past. For this, use two types of simple linear functional forms: the AR ...