1. Briefly describe the constituent elements of time series.
The constituent elements of time series are divided into four types, namely trend, seasonality, periodicity and randomness.
(1) A trend is a continuous upward or downward change in a time series over a long period of time, also known as a long-term trend;
(2) Seasonality is also called seasonal variation, which is a periodic fluctuation of time series that recurs within a year;
(3) Periodicity is also called cyclic fluctuation, which is a wave-shaped or oscillatory change around the long-term trend presented in the time series;
(4) Randomness, also known as irregular fluctuation, refers to the influence of chance factors on the time series, which makes the time series show some random fluctuations.
2. What issues should be paid attention to when using growth rate to analyze time series?
When applying the growth rate to analyze practical problems, the following points should be paid attention to:
(1) When the observed value in the time series is 0 or negative, it is not appropriate to calculate the growth rate. This is because calculating the growth rate for such a sequence either does not conform to mathematical axioms or cannot explain its practical significance;
(2) In some cases, the growth rate cannot be discussed purely in terms of the growth rate, and attention should be paid to combining the growth rate with the absolute level for analysis.
3. Briefly describe the meaning of stationary sequence and non-stationary sequence.
(1) A stationary sequence is one in which there is basically no trend. The observations in this type of series basically fluctuate at a fixed level, although the fluctuations vary in different time periods, but there is no certain pattern. Its fluctuation can be regarded as random.
(2) Non-stationary sequence is a sequence containing trend, seasonality or periodicity, which may only contain one of these components, or may be a combination of several components. Therefore, the non-stationary sequence can be divided into a sequence with a trend, a sequence with a trend and a seasonality, and a composite sequence composed of several components.
4. Briefly describe the forecasting procedure of time series.
When forecasting a time series, it usually includes the following steps:
(1) Determine the components contained in the time series, that is, determine the type of time series;
(2) Find a forecasting method suitable for this type of time series;
(3) Evaluate possible forecasting methods and determine the best forecasting scheme;
(4) Use the best forecasting scheme for forecasting.
5. Briefly describe the basic meaning of exponential smoothing method.
The exponential smoothing method is a method of weighting the past observations to obtain the forecast value. This method makes the forecast value of the t+1 period equal to the weighted average of the actual observation value of the t period and the forecast value of the t period. Exponential smoothing method is a special form of weighted average. The farther the observation time is, the smaller its weight is, and it shows an exponential decline, so it is called exponential smoothing.
The key to using the exponential smoothing method is to determine an appropriate smoothing coefficient α, because different α will have different effects on the prediction results. Generally speaking, when the time series has large random fluctuations, a larger α should be selected so as to quickly catch up with recent changes; when the time series is relatively stable, a smaller α should be selected. But in actual application, several α can be selected for prediction, and then the one with the smallest prediction error can be found as the final α value.
6. Briefly describe the forecasting steps of compound time series.
Composite sequence refers to a sequence containing trend, seasonality, periodicity and random components. For this type of sequence prediction method, the various factors of the time series are usually decomposed one by one, and then the prediction is performed. The decomposition method prediction is usually carried out according to the following steps:
(1) Identify and separate seasonal components. Computes the seasonal index to determine the seasonal component in a time series. Then the seasonal component is separated from the time series, that is, each time series observation is divided by the corresponding seasonal index to eliminate seasonality;
(2) Establish a prediction model and make predictions. Build an appropriate forecasting model for the time series from which the seasonal component has been removed, and make forecasts based on this model;
(3) Calculate the final predicted value. The predicted value is multiplied by the corresponding seasonal index to obtain the final predicted value.
7. Briefly describe the calculation steps of the seasonal index.
Taking the moving average trend removal method as an example, the basic steps to calculate the seasonal index are:
(1) Calculate the moving average (for quarterly data, use 4-item moving average, and for monthly data, use 12-item moving average), and "centralize" the result, that is, perform the moving average result again 2 The term moving average yields a "centralized moving average" (CMA).
(2) Calculate the ratio of the moving average, also known as the seasonal ratio, that is, divide each observed value of the sequence by the corresponding centralized moving average, and then calculate the quarterly (or monthly) average of each ratio.
(3) Seasonal index adjustment. Since the average of each seasonal index should be equal to 1 or 100%, if the average of the seasonal ratios calculated according to step (2) is not equal to 1, adjustments are required. This is done by dividing the mean of each season's ratios calculated in step (2) by their overall mean.