Decomposition and fluctuations time series prediction
fluctuation
Fluctuations (volatility) is the nature of the financial markets and the most common phenomenon. For investors, the volatility is an important source of earning trading profits. According to the efficient market theory, the market price will reflect the most current information. Because of an endless supply of market information, so each variety of transactions prices are constantly changing them. But for traders, they can only see the final performance fluctuate under the influence of different factors. To be more precise to analyze and forecast price volatility, traders need to change to deconstruct (decomposition), the decomposition of time sequences of different factors, and then again a combination of different factors fluctuations in the value of a future prediction time , give an overall predictive value of this point in time.
sequentially
Fluctuation time series decomposition process similar to a multiple regression equation, i.e. with a plurality of independent variables (factors) to explain a dependent variable (fluctuations). But these variables are related to price fluctuations on one or a series of specific point in time.
In general, the price of a combination of time series can be divided into the following three factors: First, the trend factor, which is a factor affecting the entire time series covering (some textbooks will further the trend factor decomposition of a cycle factor ). Followed by seasonal fluctuations factor, which is kind of factors at certain time intervals is repeated regularly appear and disappear. Finally, the randomness factor, which is a non-factors related to time. In practice, these three factors there may be one or more, or may not exist.
for example
If we want to predict bond yields, the market apparently risk-free rate of return rating and bonds belong to the trend factor. The end of the quarter, the end of the funding changes are seasonal factors. Finally, we will affect the market itself daily transactions and financial situation of supply and demand caused by classified random factor, because the supply and demand caused by a number of sporadic exchange of large sums of money, for the market is disorderly.
Advantage
The greatest benefit is the use of volatility decomposition of complex time series can be turned into a series of simple and orderly fluctuations combined to achieve predictability. Because according to the principle of Fourier transform, any periodic signal may be a series of (finite or infinite number of) a sine wave superimposed to represent. A complex time series can not be predicted simply from t0 to t1, but if we are to be decomposed into simple prediction series (factor trend fluctuation factor +) and random sequence (random factor), because the expected value of the random factor is 0, then we just need a predictable sequence of predicted results t1, plus an expected value for the random factor of zero, then the result becomes this complex time series theoretically optimal unbiased expectations.
Disadvantaged
Although the theory of fluctuations decomposition is perfect, but in the actual application is very skinny. In actual operation, there are some fluctuations tend to decompose inherent flaws. First, the identification of the seasonal factor uncertainty. Either by empirical predictions themselves to specify the expected seasonal (eg quarterly or month to identify), or use the software automatically recognizes. But no matter what kind of identification was out seasonal factors, there may be logical or reasonable (excessive data mining), or to identify factors that influence it has little significance low.
Secondly, although the randomness factor in the overall time series of mean and a point in time in the future expected value is 0, but specific to a certain specific point in time, random events it is possible to produce a more significant impact (such as a few years ago Everbright more famous "own means" event).
Finally, as the "efficient market hypothesis" and "reflexivity principle of" implied truth: when a profit model is well known, when the profitability of this model will be diluted too many users and even disappear.
references
Zhang Chengsi (2012) Financial Econometrics:.. (. Pp 24-225). Time series analysis perspective of China Renmin University Press
Source: quantitative investment club
Further Reading:
1. a quantitative strategist Confessions (Good text strongly recommended)
2. classic quantitative trading strategies available in the market are here! (Source)
3. futures / stock data Daquan query (History / real-time / Tick / finance, etc.)
5. From the high-frequency trading to quantify, can not read five books
6. HFT four factions Big Secret
