Question

The time series component that reflects variability during a single year is called

Answer 1

Answer:

The time series component that reflects variability during a single year is called the seasonal component.

Explanation:

From the above question,

They have given :

The time series component that reflects variability during a single year is called the seasonal component. This component usually reflects patterns of demand that occur throughout the year, such as increasing demand during the holiday season or increasing demand during the summer months. The seasonal component can be used to model short-term fluctuations in demand and help to predict future sales or other types of demand.

Seasonal component is used to better understand the short-term fluctuations in demand over the course of a year, and to better predict future sales. It can help to identify trends in demand that can be used to inform marketing and pricing decisions. It can also be used to identify opportunities for new products or services in order to better meet customer needs.

This component is useful in forecasting future behaviour as it can take into account seasonal fluctuations in demand. The seasonal component can be used to help understand seasonality in data, and can also be used to predict future behaviour.

It is important to note that the seasonal component is different from the trend component, which is the component that reflects long-term changes in the data. The seasonal component can be further broken down into monthly, weekly, and even daily components, depending on the nature of the data.

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Answer 2

Answer:  The time series component that reflects variability during a single year is called cyclical.

Explanation:

A cyclic pattern exists when data exhibit rises and falls that are not of fixed period. The duration of these fluctuations is usually of at least 2 years. Think of business cycles which usually last several years, but where the length of the current cycle is unknown beforehand.

Many people confuse cyclic behaviour with seasonal behaviour, but they are really quite different. If the fluctuations are not of fixed period then they are cyclic; if the period is unchanging and associated with some aspect of the calendar, then the pattern is seasonal. In general, the average length of cycles is longer than the length of a seasonal pattern, and the magnitude of cycles tends to be more variable than the magnitude of seasonal patterns.

Cyclic ARMA models

The class of ARMA models can handle both seasonality and cyclic behaviour. An ARIMA (p,q)(p,q) model can be cyclic if p>1p>1 although there are some conditions on the parameters in order to obtain cyclicity. For an AR(2),

where y_t = c + \phi_1y_{t-1} + \phi_2y_{t-2} + \varepsilon_tyt​=c+ϕ1​yt−1​+ϕ2​yt−2​+εt​ and \varepsilon_tεt​ is white noise,

cyclic behaviour is observed if {\phi_1^2+4\phi_2 < 0}ϕ12​+4ϕ2​<0.

In that case, the average period of the cycles is

The time series component that reflects variability during a single year is called cyclical.

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