Sharpe Ratio

Beta

Jensen's Alpha

Unit Root

Augumented Dickey-Fuller (ADF) Test

Weiner Process

The Random Walk of Stock Market

Simulating Geometric Brownian Motion

Wiener Process Implications

The Augmented Dickey-Fuller (ADF) test is a common statistical test used to determine whether a given time series is stationary or not. Stationarity is a crucial concept in time series analysis, as many forecasting methods assume that the time series is stationary. A time series is said to be stationary if its statistical properties, such as mean and variance, remain constant over time.

In the last chapter, We have conducted ADF test on SBIN. And We had found this results –

` ````
```ADF Statistic: -3.564168196716654
p-value: 0.006484183313370225

Here’s a detailed breakdown of the results obtained from the ADF test on SBIN’s closing prices:

**ADF Statistic:**

- The ADF statistic is a negative number, which is -3.564 in this case.
- The more negative this statistic is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence.
- The value of -3.564 suggests a significant level of stationarity in the time series data of SBIN’s closing prices.

**P-value:**

- The p-value obtained is 0.00648.
- The p-value is a crucial aspect in hypothesis testing. It indicates the probability of observing the test statistic if the null hypothesis is true.
- In the context of the ADF test, the null hypothesis is that the time series has a unit root, implying it is non-stationary.
- A smaller p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
- The p-value of 0.00648 is less than 0.05, indicating that we can reject the null hypothesis of a unit root at the 5% significance level. This means there is sufficient evidence to conclude that the time series is stationary.

**Implications:**

- Finding that the SBIN’s closing price time series is stationary implies that it has a constant mean and variance over time, and it is not influenced by a trend or seasonality.
- This is valuable information because many time series forecasting techniques require the data to be stationary.
- Furthermore, the stationarity of SBIN’s closing prices suggests that past price behavior is a good indicator of future price behavior, which could be useful for predictive modeling.

**Further Analysis:**

- Although the ADF test provides valuable insights into the stationarity of the time series, it’s prudent to complement this analysis with graphical methods such as plotting the time series data, and the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots.
- Additionally, other statistical tests like the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test can also be used to confirm the findings from the ADF test.

**Statistical Significance:**

- The statistical significance of the test is crucial for making reliable inferences. In this case, the ADF test suggests statistical significance at the 5% level, which is a common threshold used in practice.

- The p-value is a measure of the strength of the evidence against the null hypothesis. It provides the probability of observing a test statistic as extreme as the one computed, given that the null hypothesis is true.
- In the ADF test, the null hypothesis states that the time series has a unit root (i.e., is non-stationary). A lower p-value (typically ≤ 0.05) suggests that the evidence against the null hypothesis is stronger, allowing us to reject the null hypothesis in favor of the alternative hypothesis (that the time series is stationary).

A hypothesis is a statement or claim regarding a characteristic of one or more populations. It’s a kind of educated guess or assertion that you’re looking to either support or disprove through data analysis.

The null hypothesis (\(H_0\)) is a specific statement made about a population parameter. The null hypothesis is often a statement of no effect or no difference.

For example, in the ADF test, the null hypothesis is that the time series has a unit root (i.e., is non-stationary).

In the context of the Augmented Dickey-Fuller (ADF) test, the null hypothesis posits that the time series data possesses a unit root, signifying that it is non-stationary.

A unit root suggests that the time series data is influenced by a stochastic trend, making it unpredictable and difficult to model.

**When a time series has a unit root, it exhibits a random walk behavior, where each value in the series is a reflection of its past value plus a random shock. **

The null hypothesis in the ADF test is crucial as it sets the stage for testing whether or not the time series data is stationary, which in turn impacts the appropriateness of employing certain statistical models or forecasting techniques on the data.

Post a comment