# Stationary Process (No Trend)

Figure 5-1: Stationary Process is corresponding to Pattern (1, 1) in the table.

Simply speaking stationary process is the horizontal pattern where price series fluctuates around a constant mean. As you might guess, it is a mathematical term. You might be unfamiliar with this term. However, it is no point to reinvent the wheel again when the wheel is already there. Hence, we will stick with this term. Stationary process describes the pattern (1, 1) best on the Table in Figure 3-3. If price series is exhibiting stationary process, you will not able to observe a notable trend in the prices series.  On the other hands, if the price series are non-stationary, then the variance and mean will change over time. You have to understand that having constant mean or not can change your trading outcome dramatically. Among many mathematical and institutional trader, stationarity is one fundamental factor in deciding their trading strategy. To give you better idea about stationary, we have removed trend in EURUSD artificially in Figure 5-2. You can see that the price series is always try to go back to its mean in Figure 5-2. The original EURUSD series will never look like this because they have trend as shown in Figure 5-3.

Figure 5-2: De-trended EURUSD Series Daily timeframe is a good example of stationary series.

Figure 5-3: Original EURUSD Series Daily timeframe. This is a good example of non-stationary series.

White noise series are another example of stationary because they are fluctuating around the mean. In contrast, random walk series in Figure 4-2 does not fluctuate around the one level like white noise series does. Therefore, random walk series in Figure 4-2 is not stationary. Very few commodity and stock price series can exhibit strong stationarities in its original form. Most of time, many Stock, and currency price series are non-stationary meaning that they are not coming back to the mean. In fact, you can find many ratio series are stationary. For example, the ratio series of S&P 500 and earning is well known stationary series (Figure 5-4). Typically, the ratio of S&P 500 and its earning tends to revert to the mean. Many traders make use of this fact for their trading. In addition, many ratio series of currency pairs can be stationary too. This assumption is the basis for the popular Pairs Trading.

Normally the very first step of analysing any financial price series involves checking if they are stationary or non-stationary. This horizontal pattern is very important in determining your trading strategy. For example, if any price series exhibit stationary process, then mean reversion-trading strategy is good. If the price series are non-stationary, then choice of trading strategy is dependent on type of dominating regularities in the financial price series. Now you wander how to detect stationarity of the price series. In fact, some well-trained eyes can tell the stationary by visual inspection from the chart. You will mostly focus on looking for the horizontal pattern. However, it is common to use a statistical testing to check the stationarity of the price series.

Figure 5-4: S&P 500 Price/Earning series. This is a good example of stationary process.

It is less common to see any financial price series in stocks and forex market exhibiting strong stationary process. Having said that, if any financial price series show stationarity, then it is extremely easy to trade with this series. Therefore, you should always check if such an opportunity exists first before using any other complex trading strategy. For the stationary price series, trader can use the typical mean reversion trading strategy. For example, one can buy if the price stays below three standard deviations from the mean. One can sell if the price stays above three standard deviations from the mean. Sometimes one can use four standard deviation rule instead of three standard deviation rule. You can look at ratio for the potential trading opportunities. For example, Price/Earnings ratios are popular ways to trade Stock market. Trader can also use Price/Price ratio too for Pairs trading opportunities.

Figure 5-5: Mean reversion trading scenario for stationary price series.

Analytical Note

You can use several different techniques to confirm stationarity of the price series. Mostly the testing procedures are based on the statistical Hypothesis Testing. The commonly used one is the Augmented Dickey Fuller test. Some other techniques include Philipps-Perron test, KPSS test and Variance Ratio test. In addition, Hurst Exponent might be used to check the stationary characteristics of the price series too. Since price series might show stationarity during some period of the data set temporally, it is important to use the entire data set to test stationarity. It is often better to use more than one techniques to confirm stationarity for better accuracy. If you have no access to these testing tools, then you can simply make the visual inspection on your chart.

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