[Casual note] Time series prediction

本文主要是介绍[Casual note] Time series prediction，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

Time series prediction

- 在主要feature是时间时用的比较多。如果有很多额外的feature，考虑深度模型
- Trend： 长期的趋势
- Seasonality：季节性
- Cyclicity：周期性 比如经济周期
- Irregularity：unpredictable factors。最好在数据层面就剔除掉

# Before forecasting
- Make sure the series is stationary : devoid of seasonality and trend, the mean and variance is nearly constant.
- Data analysis, decompose the four factors
- check if the 'random' component is stationary. Null hypothesis : non-stationary. Given this hypothesis, the possiblity to have the current data is the p-value.

# Models
- ARMA : Auto Regression (使用历史值回归) + Moving Average(使用历史均值回归)
- ARIMA: ARMA by 增量数据

# Correlation test
ACF：auto-correlation function. x=2, y is the correlation between x_t and x_{t-2}.

PACF: 在ACF中, x_t和x_{t-2}的correlation中间还有x_{t-1}的影响。所以有了partial ACF，把x_{t-1}的影响去掉. 具体涉及一些统计知识，需要进一步挖掘

ACF和PACF的结果指导了ARIMA的参数选择。ACF图结合significance level看。

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