Discover how to model, interpret, and forecast time series data. Learn about stochasticity, stationarity, ARIMA models, and decomposition. Gain skills to explore, model, and forecast using Python.

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Time series are all around us, from stock prices and weather forecasts to economic trends and medical diagnoses. This course is designed to equip you to effectively model, interpret, and forecast time series.

In this course, you’ll learn time series analysis concepts, such as stochasticity, stationarity, and autocorrelation. You’ll analyze the time series by computing its various moments and by visualizing it using histogram and density plots. Next, you’ll decompose the time series into its trend, season, and cycle components. You’ll then learn about linear time series models, including autoregressive (AR) processes, moving average (MA) processes, ARMA, and ARIMA. You’ll fit these models on data and forecast the future and finish with evaluating the models using various goodness of fit criteria. 

By the end of this course, you’ll have a solid foundation in univariate time series analysis and the skills to explore, model, and forecast time series data using Python.

An Introduction to Time Series

$I(1)$ is another way to refer to a random walk model with drift.

It is a process with a deterministic trend that becomes stationary when we subtract the expected value of the process. 

It is a process that can be made stationary by taking first differences.

It is a process that becomes stationary when we subtract its random component. 

What is an integrated process of order 1, $I(1)$? 

What is an integrated process of order 1, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I(1)</annotation></semantics></math>I(1)?

**(Select all that apply.)** How can you calculate the returns of a price series, $P_t$? 

(Select all that apply.) How can you calculate the returns of a price series, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">P_t</annotation></semantics></math>Pt​?

By accepting the null hypothesis that the process is a random walk, we conclude that the process is not $I(1)$.

By rejecting the null hypothesis that the process is white noise, we conclude that the process is not $I(1)$.

By rejecting the null hypothesis that the process is a random walk, we conclude that the process is $I(1)$.

By rejecting the null hypothesis that the process is a random walk, we conclude that the process is not $I(1)$.

What's the idea behind the standard Dickey-Fuller (DF) test for integration? 

What’s the idea behind the standard Dickey-Fuller (DF) test for integration?

The model in the standard version of the test might fail to capture all time dynamics in the series. 

The error term in the model in the standard version, $\epsilon_t$, might not be white noise in practice. 

The $\beta$ parameter in the standard model might conflate information on the process that is not directly attributable to $y_{t-1}$. 

Why is the Augmented Dickey-Fuller (ADF) test recommended over the standard Dickey-Fuller (DF) test?

Why is the Augmented Dickey-Fuller (ADF) test recommended over the standard Dickey-Fuller (DF) test?

**(True or False)** The shaded area in a correlogram tells us which autocorrelation coefficients are statistically greater than 0. 

(True or False) The shaded area in a correlogram tells us which autocorrelation coefficients are statistically greater than 0.

The autocorrelation coefficient of order $j$ accounts for the effect of all lags between $t$ and $t-j$. The partial autocorrelation coefficient doesn't.

The partial autocorrelation coefficient of order $j$ accounts for the effect of all lags within a window of size $j$ centered at $t$. The autocorrelation coefficient doesn't.

The partial autocorrelation coefficient of order $j$ accounts for the effect of all lags between $t$ and $t-j$. The autocorrelation coefficient doesn't.

The autocorrelation coefficient of order $j$ accounts for the effect of all lags within a window of size $j$ centered at $t$. The partial autocorrelation coefficient doesn't.

What is the difference between the autocorrelation coefficient and the partial autocorrelation coefficient of a series, $y_t$? 

What is the difference between the autocorrelation coefficient and the partial autocorrelation coefficient of a series, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">y_t</annotation></semantics></math>yt​?

It uses a function of the sum of autocorrelation coefficients of a series to determine if there is any serial correlation of any sort in the series. 

It uses the cumulative distribution function of the normal distribution in the search for any serial correlation in the series.

It uses a function of the sum of autocorrelation coefficients of a series to determine if the series is integrated.  

The sum of the autocorrelation coefficients of a series up to lag $k$ has to be between 0 and 4 to reject the null hypothesis of no serial autocorrelation. 

Why do we say that the Ljung-Box (LB) test has a cumulative nature? 

Why do we say that the Ljung-Box (LB) test has a cumulative nature?

$\lambda$, the smoothing parameter of the minimization problem

$k$, the number of observations to either side of the point that we want to smooth out 

$\rho$, the autocorrelation coefficient within the window that we calculate the moving average for 

**(Select all that apply.)** What are the parameters of a moving average filter? 

(Select all that apply.) What are the parameters of a moving average filter?

$\lambda = 6.25$, as there are five years of data.

$\lambda = 12900$, as sales are highest during the month of December due to Christmas.

A value for $\lambda$ cannot be determined without further analysis.  

The Hodrick-Prescott filter is not suitable for seasonal data, so it should not be used for this analysis.

Suppose you have data on daily sales from a firm in the retail sector for the past five years. The data shows a heavy yearly seasonal component, as most of its sales happen at Christmas. You want to know if sales have gone up in the past five years, so you decide to decompose the series using the Hodrick-Prescott filter. What value for the lambda parameter, $\lambda$, should you use? 

Select the most correct option.

Suppose you have data on daily sales from a firm in the retail sector for the past five years. The data shows a heavy yearly seasonal component, as most of its sales happen at Christmas. You want to know if sales have gone up in the past five years, so you decide to decompose the series using the Hodrick-Prescott filter. What value for the lambda parameter, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math>λ, should you use?
Select the most correct option.

The properties of time series

The properties of time series

Quiz yourself on the properties of time series.

Introduction to Time Series

The Basics of Time Series

Exploring Data

The Properties of Time Series

ARIMA Models

On Prediction

Choosing, Fitting, and Evaluating Models

Conclusion

Appendix

What have you learned?

Quiz