Steps in Time Series Analysis
Time series analysis is a statistical technique used to predict future values, mainly by observing and studying the trends and patterns of data changes over time. The steps in time series analysis include data collection, data visualization and correlation analysis, model selection and fitting.
1, data collection:
First, the time series dynamic data of the observed system is obtained through observation, survey, statistics and sampling. This is the basis of the whole analysis process, the quality and accuracy of the data has a direct impact on the analysis results.
2, data visualization and correlation analysis:
Collected dynamic data will be plotted into a correlation diagram, correlation analysis, and derive the autocorrelation function. The correlation graph can visualize the trend and cycle of data changes, and also can find the jump point and inflection point.
The jump point is an observation that is inconsistent with other data. If the jump point is a correct observation, it should be taken into account in modeling, and if it is an anomaly, the jump point should be adjusted to the desired value. The inflection point, on the other hand, is the point at which the time series suddenly changes from an upward trend to a downward trend. If there is an inflection point, a different model must be used to fit the time series in segments when modeling.
3. Model Selection and Fitting:
Based on the second step, a suitable stochastic model is selected for curve fitting, i.e., a generalized stochastic model is used to fit the observed data of the time series.
For short or simple time series, trend and seasonal models plus errors can be used for fitting. For smooth time series, a generalized ARMA model (autoregressive sliding average model) and its special cases such as autoregressive model, sliding average model, or combined ARMA model can be used for fitting.
The ARMA model is generally used when there are more than 50 observations. For non-stationary time series, it is necessary to carry out the difference operation first, to be transformed into a stationary time series, and then use the appropriate model to fit this difference series.
The above are the basic steps of time series analysis, each step has its own unique role, one without the other. Through these steps, we can effectively analyze and forecast time series data to provide strong support for decision-making.
Time Series Analysis
Time Series Concept: A series of successive observations of the same phenomenon at different times
Formally consisting of two parts: the time to which the phenomenon belongs, and the observations of the phenomenon at different times
The time of the arrangement can be yearly, quarterly, monthly…
The classification of time series:
1. Absolute number sequence:
A series of absolute numbers arranged in chronological order; the most basic form of expression; reflecting the absolute level achieved at different times (period sequence, the order of totals over a period of time, point-in-time sequence, the order of totals at a particular moment in time)
2. Relative series: a series of relative numbers arranged in chronological order
3. Mean series: a series of averages arranged in chronological order
Time series of the preparation of the principle:
Time duration consistency
The overall scope of consistency
Consistent content of indicators
Consistent method and caliber of calculation
I. Comparative analysis of time series
1. Level of development: the observation of the phenomenon at different times; describes the phenomena level achieved at a given time;
2. Mean level of development: the average of the values taken by the phenomenon at different times, also known as the average of the sequences; describes the general level of the phenomenon achieved over a period of time; (different types of sequences are selected for different methods of computation-periods, consecutive time-points (day-by-day ordering), unequally spaced time-points (weighted), equidistant time-points (the special case of unequal distance );
#Relative number: division of two absolute numbers
#Sequential mean of relative numbers: division of the mean of the numerator by the mean of the denominator
3. Growth: the difference between the level of the reporting period and the level of the base period, which describes the absolute amount of growth of the phenomenon over the period under observation
p>Divided into period-by-period growth (the difference between the level of the reporting period and the level of the previous period) and cumulative growth (the difference between the level of the reporting period and the level of a fixed period) – the sum of the period-by-period growth is equal to the cumulative growth at the end of the period
4. Mean growth: the average of the period-by-period growth, which is equal to the sum of the period-by-period growth / number of the period-by-period growths (i.e., the number of observations -1)
1. Developmental velocity: the ratio of the level of the reporting period to the level of the base period, which indicates the relative degree of development of the phenomenon over the period of observation,
Divided into the cyclic developmental velocity (the ratio of the level of the reporting period to the level of the previous period) and the periodic developmental velocity (the ratio of the level of the reporting period to the level of a fixed period of time) – the product of the cyclic developmental velocity is equal to the maximum of the cyclic developmental velocity (the ratio of the level of the reporting period to the level of the previous period). The product of the ring development rate is equal to the final periodic development rate;
2. Growth rate (growth rate): the ratio of the growth volume to the level of the base period, which indicates the degree of relative growth of the phenomenon,
equal to the rate of development-1; divided into the ring growth rate and the fixed-base growth rate;
3. Average development rate : the average of the development rate of each ring during the observation period, indicating the average development of the phenomenon throughout the observation period the degree of change (geometric method of calculating the average)
4. Average growth rate: equal to the average development rate – 1
Two, the trend analysis of the time series
Can be used to move the average, the method of least squares and so on…
Three, seasonal variation analysis
Seasonal variation: the phenomenon in a year with the change of seasons to form a regular change; the intensity of change in each year is more or less the same, and no year to reappear;
Expansion: a year due to the impact of social, political, economic and natural factors, the formation of a certain period of time as a cycle of regular repetition of changes. change;
Measurement purpose: to determine the past seasonal pattern of change of the phenomenon, eliminating the seasonal factors in the time series;
Analytical principle: the law of seasonal change is summarized into a typical seasonal model; seasonal model consists of seasonal indices; the average of seasonal indices is equal to 100 percent; the degree of seasonal change is determined according to the deviation of seasonal indices from their mean The degree of seasonal variation is determined according to the degree of deviation of the seasonal index from its average;
Seasonal index: 1. Reflects the relative number of seasonal variation; 2. Calculated on the basis of the average of the annual or seasonal information; 3. Average is equal to 100%; 4. The further the index is away from the average of its seasonal variation the greater the degree of change; 5. Average over the same period of time and trend elimination
Average over the same period of time:
Calculate the seasonal index by simple averaging based on the original time series
Assuming that the time series has no significant long-term trend and cyclical fluctuations
Steps: 1. Calculate the mean over the same period of time; 2. Calculate the mean of the total season of all data; 3. Calculate the seasonal index S = mean over the same period of time / mean of the total season
Trend-exclusion method: <
First, the long-term trend in the time series to be eliminated, in the calculation of the seasonal index
Steps: 1. Calculate the trend value of the moving average Y; 2. Eliminate the trend value of the series Y/T; 3. Calculate the seasonal index in accordance with the above method
Four moving averages and then two moving averages (four to do the year) Remove the season, the two more stable)
Seasonal variation adjustment: the seasonal variation is removed, the method is the river source time series divided by the corresponding seasonal index
Four, cyclic volatility analysis
Cyclic volatility: nearly regular from low to high and then from high to low weekly changes; different from the trend changes, he is not in a single direction of the Continuous movement, but the alternating fluctuations of the rise and fall; different from seasonal fluctuations, its changes have no fixed rules, changes in the cycle of more than a year, and the length of the cycle varies
Purpose is to explore the regularity of the phenomenon
Measurement method: take the residual method
Calculation steps: 1. first eliminate the trend value, to find no Long-term trend data; 2. Eliminate seasonal variations (original data/seasonal index) to obtain the relative number of cyclic and irregular fluctuations; 3. Move the results to eliminate irregular fluctuations by moving the average, i.e., obtaining the cyclic fluctuation value.