Question

Describe the following terms

a) stationary time series

b) seasonal time series

c) box test ( clearly define your notation and the null and alternative hypotheses)

Answer 1

answer:

a) stationary time series:

a stationary procedure is a stochastic procedure whose unrestricted joint likelihood circulation does not change when moved in time.Consequently, parameters, for example, mean and difference additionally don't change after some time.

Since stationarity is a presumption basic numerous measurable strategies utilized in time arrangement examination, non-stationary information is frequently changed to end up stationary. The most well-known 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 momentary impacts after which the variable inclines toward a deterministically developing (non-steady) 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. A critical kind of non-stationary process that does exclude a pattern like conduct is a cyclostationary procedure, which is a stochastic procedure that differs consistently with time.

b) seasonal time series:

regularity is the nearness of varieties that happen at explicit ordinary interims not exactly a year, for example, week by week, month to month, or quarterly. Regularity might be brought about by different elements, for example, climate, excursion, and occasions and comprises of intermittent, monotonous, and for the most part customary and unsurprising examples in the dimensions of a period arrangement.

Regular variances in a period arrangement can be appeared differently in relation to recurrent examples. The last happen when the information displays rises and falls that are not of a settled period. Such non-regular variances are typically because of financial conditions and are frequently identified with the "business cycle"; their period for the most part reaches out past a solitary year, and the vacillations are as a rule of no less than two years.

Associations confronting regular varieties, for example, frozen yogurt merchants, are frequently keen on knowing their execution with respect to the ordinary occasional variety. Regular varieties in the work market can be credited to the passage of school leavers into the activity showcase as they intend to add to the workforce upon the culmination of their tutoring. These ordinary changes are of less enthusiasm to the individuals who contemplate business information than the varieties that happen because of the fundamental condition of the economy; their attention is on how joblessness in the workforce has changed, regardless of the effect of the customary occasional varieties.

It is important for associations to recognize and gauge regular varieties inside their market to enable them to get ready for what's to come. This can set them up for the brief increments or diminishes in labor necessities and stock as interest for their item or administration changes over specific periods. This may require preparing, occasional support, etc that can be sorted out ahead of time. Aside from these contemplations, the associations need to know whether variety they have encountered has been pretty much than the normal sum, past what the standard regular varieties represent.

c) box test :

The Ljung–Box test may be defined as:

H₀: The data are independently distributed (i.e. the correlations in the population from which the sample is taken are 0, so that any observed correlations in the data result from randomness of the sampling process).

H_a: The data are not independently distributed; they exhibit serial correlation