Quantitative Investment Time Series: Basic Theory

How can

mathematics, statistics or machine learning help us improve the efficiency of transaction analysis ? ——Intelligent investment research.

This question is more meaningful than hoping that artificial intelligence will replace our trade fair, at least for now. In many fields, deep learning seems to be doing well, but whether it is the efficiency of learning or the nature of learning, AI is far too far behind humans, not to mention that human beings such as investment cannot tell whether it is science or Art things.

In investment, our most common data is the time series of transactions, and the most common data set is daily OHLCV data.

Time series analysis belongs to the statistical category of , whether it is one-dimensional time series or multivariate time series analysis, it is within the scope of the statistics department. But because of its deep connection with economics, it is generally used as an important basis for econometrics .

Quant itself can be divided into two categories:

1. finance and econometrics economic field 15 is relatively less quantified than span13, which is biased towards time series analysis of span13.Therefore, the general quantitative investment starts with time series analysis.
2. Machine learning is another way to do quant, which is parallel to time series analysis.

There are two modes in the time series, one is mean regression; the other is trend following (momentum effect).

Mean regression: If the time series is stationary, there is a mean, and the product price operates around the mean. If the time series is a random walk, the state of the next moment cannot be judged based on the past and is independent of the past price, then it is impossible to build a statistical model in the securities market to make money. The price of a single stock is probably a random walk. However, a stock portfolio may not be random walk (smooth), so there is a need for research. —— A "stable" "arbitrage" investment portfolio can be constructed through statistical methods.

In the time series, there are trends, cycles, and autocorrelation, and the rest are random walks.

Stationarity is the basis of time series analysis. is strictly balanced. To put it bluntly, returns from the same probability distribution : for all , , span13, span13, and span13 are not the same with span13 and span13. Change of time.Such a time series is (strictly) stationary. But this condition is too strict, generally we pay attention to weakly stable , that is, the mean and the variance of have (second-order) stationarity. But even if it is weakly stable, it is not easy for financial time series to meet the standard. Therefore, we need to shorten the time span of or model the volatility through a more complex nonlinear model (such as GARCH).

More advanced time series models to model autocorrelation. In this regard, the autoregressive model (AR) and the moving average model (MA) , and their combination-the autoregressive moving average model (ARMA)-are both very powerful tools.

P-order autoregression, which is well understood, is the current rate of return, using the past P period to linearly fit:

The ARIMA model is a model that solves non-stationary series on the basis of the ARMA model.Therefore, the original sequence is differentiated in the model.

It is intuitive to apply time series analysis to quantitative investment. Because the first thing we get is time series related data, the basic financial assumption of technical analysis is that history can be repeated, that is, history contains patterns that can be repeated in the future. If this is the case, time series analysis models will be very useful.

But the fact is, don't expect an indicator or model to directly solve the problem, but to help us better understand the data.

For example, the historical rate of return is only one aspect, what about the combined valuation situation? Combined with the RSRS indicator.

(Public account: Seven years to achieve freedom of wealth ( ailabx ), thinker, actionist; use numbers to say funds, use funds as investment portfolios, and practice the road to wealth freedom)

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