1. What is an ARIMA model? Why might ARIMA models be considered particularly use
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Question
1. What is an ARIMA model? Why might ARIMA models be considered particularly useful for financial time series?
2. Describe the steps that Box and Jenkins (1970) suggested should be involved in constructing an ARMA model.
3. ‘Given that the objective of any econometric modeling exercise is to find the model that most closely “fits” the data, then adding more lags to an ARMA model will almost invariably lead to a better fit. Therefore, a large model is best because it will fit the data more closely.
Comment on the validity (or otherwise) of this statement.
4. What is meant by the term stationary, as applied to a time series model? Explain how the notation I(0) and I(1) is related to the concept of stationarity. Give one example of a stationary model and one of a non-stationary model.
Explanation / Answer
1:
ARIMA remains for Autoregressive Integrated Moving Average models. Univariate (single vector) ARIMA is a determining method that undertakings the future estimations of an arrangement construct completely with respect to its own particular latency. Its fundamental application is in the zone of here and now anticipating requiring no less than 40 verifiable information focuses. It works best when your information displays a steady or predictable example after some time with a base measure of exceptions. At times called Box-Jenkins (after the first creators), ARIMA is generally better than exponential smoothing strategies when the information is sensibly long and the connection between's past perceptions is steady. On the off chance that the information is short or exceptionally unpredictable, at that point some smoothing technique may perform better. In the event that you don't have no less than 38 information focuses, you ought to think about some other strategy than ARIMA.
Fundamental Concepts:
The initial phase in applying ARIMA approach is to check for stationarity. "Stationarity" suggests that the arrangement stays at a genuinely steady level after some time. On the off chance that a pattern exists, as in most monetary or business applications, at that point your information isn't stationary. The information ought to likewise demonstrate a steady change in its variances after some time. This is effectively observed with an arrangement that is vigorously regular and developing at a speedier rate. In such a case, the high points and low points in the regularity will turn out to be more sensational after some time. Without these stationarity conditions being met, huge numbers of the figurings related with the procedure can't be registered.
ARIMA models are of specific use for financial series because of their adaptability. They are genuinely easy to assess, can frequently deliver reasonable forecasts, and above all, they require no learning of any basic factors that may be required for more "conventional" econometric investigation. At the point when the information are accessible at high frequencies, we can at present utilize ARIMA models while exogenous "logical" factors (e.g. macroeconomic variables, accounting ratios) might be imperceptible at any more than month to month interims, best case scenario.
2:
The Box-Jenkins method was proposed by George Box and Gwilym Jenkins in their fundamental 1970 textbook Time Series Analysis: Forecasting and Control.
The approach begins with the supposition that the procedure that created the time arrangement can be approximated utilizing an ARMA display on the off chance that it is stationary or an ARIMA show in the event that it is non-stationary.
The 2016 fifth version of the course reading alludes to the procedure as a stochastic model building and that it is an iterative approach that comprises of the accompanying 3 stages:
1. Identification - Utilize the information and all related data to help choose a sub-class of model that may best condense the information.
2. Estimation - Utilize the information to prepare the parameters of the model (i.e. the coefficients).
3. Diagnostic Checking - Assess the fitted model with regards to the accessible information and check for territories where the model might be progressed.
3: In ARMA (p,q) process, there will be "p" auto-regressive and "q" average moving terms.
Applying more lags allows varying amounts of recent history to be brought into the forecast. Lagging of independent variables is also necessary in order for the regression model to be able to predict the future ,i.e., to predict what will happen in period "t" based on knowledge of what happened up to period "t-1".
Using lags of the stationary variables helps to stationaize the variables.
4:
In mathematics and statistics, a stationary process (a.k.a. a strict(ly) stationary process or strong(ly) stationary process) is a stochastic procedure whose unequivocal joint likelihood dissemination does not change when moved in time. Thus, parameters, for example, mean and fluctuation, on the off chance that they are available, likewise don't change after some time.
Since stationarity is a presumption basic numerous measurable strategies utilized as a part of time series analysis, non-stationary information is regularly changed to end up stationary. The most widely recognized reason for infringement of stationarity is a pattern in the mean, which can be expected either to the nearness of a unit root or of a deterministic pattern. In the previous instance of a unit root, stochastic stuns have perpetual impacts and the procedure isn't mean-returning. In the last instance of a deterministic pattern, the procedure is known as a pattern stationary process, and stochastic stuns have just transient impacts after which the variable inclines toward a deterministically developing (non-consistent) mean.
A pattern stationary process isn't entirely stationary, however can without much of a stretch be changed into a stationary procedure by evacuating the basic pattern, which is exclusively an element of time. So also, forms with at least one unit roots can be made stationary through differencing. An essential kind of non-stationary process that does exclude a pattern like conduct is a cyclostationary procedure, which is a stochastic procedure that shifts consistently with time.
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