Time Series Quiz #1 Actual Exam With Complete Questions With Correct Answers.

Time Series - How is it denoted? - correct answer A *collection of data points* corresponding to temporal measurements of some quantitative variable. Ex: Hourly website traffic, daily rainfall, monthly sales, quarterly revenue, annual crime rates Denoted as: {y₁, y₂, ... , y_T} where y_t represents the t-th observation of the variable y, t = 1,2,..,T --> time is always discrete here T/F: Swapping rows arbitrarily will fundamentally change the data with Time Series - correct answer True Time Series Plot - correct answer A scatterplot of y (variable) versus t (time), with adjacent points connected by a straight line. Clearly displays the relationship between the variable y and time. Time Series Analysis - correct answer Typically refers to *modeling* the relationship between the variable y and time Time Series Model - general form - use - correct answer Characterizes the relationship between y_{t+1} and {y₁, y₂, ..., y_t} --> between a point in time and all the points in time before it In general, a model will take on the form: y_{t+1} = f(y₁, y₂, ..., y_t) We use such a model to *predict* the value of y_{t+1} given the history {y₁, y₂, ..., y_t} already observed. Forecasting - correct answer Making predictions using time series model When forecasting, the further into the future we go, the [more/less] certain we are. This [widens/narrows] our prediction intervals. - correct answer less certain widens our intervals At a very general level, we can think of Time Series Analysis and Forecasting as: - correct answer Trying to understand the past to predict the future Two types of time series models - correct answer 1. Univariate - Future values of Y are forecasted using ONLY knowledge of past values of Y 2. Multivariate - Future values of Y are forecasted using past values of Y AND one or more other predictor variables X₁, X₂, ... When could adding a predictor variable be helpful? - correct answer A predictor variable could be helpful if its pattern with time looks *similar or inverse* to the OG relationship you're looking at What are the three important features of a time series? - correct answer 1. Serial Correlation 2. Trend 3. Seasonality Serial Correlation - quantified by? - correct answer The phenomena that observations closer together in time tend to be more similar than observations farther apart in time Serial correlation is quantified by the *autocorrelation function* - With data with serial correlation, we would see a high autocorrelation for a small lag, and a small autocorrelation for a large lag Autocorrelation function of lag x - correct answer Autocorrelation of lag x = corr(y_{t}, y_{t+x}) ACF Plots - correct answer plots of the autocorrelation function corr(y_{t}, y_{t+h}) vs lag h --> lag is on the x-axis - the height of the line is the correlation - blue lines are the significance level How can we visualize autocorrelation/serial correlation? - correct answer We can visualize the extent of autocorrelation in a given time series using *ACF p