Predictive Analytics Quiz Seven

What is stationarity?

When the mean, variance, and covariance remain constant throughout the entire series.

What is strict stationarity?

The entire distribution is unchanged over time and the statistical properties of the series are completely time-invariant.

What three conditions needs to be met for a time series to be considered weak (or second-order) stationarity?

1. Constant Mean (mean remains the same over time)

2. Constant Variance (variance of the series doesn’t change over time)

3. Constant Covariance (How similar two values are depends only on the time gap between them — not the exact days themselves.)

What is referred to as “the range of fluctuation”?

A constant variance

What does the following refer to: “the “pattern” of similarity is stable over time?

A constant covariance

When does a model work better?

When the underlying data-generating process is stable.

When a series is non-stationary, when do predictions become unreliable?

1. Trends or shifting levels confuse the model

2. Volatility changes distort error terms

3. Relationships between past and future values are inconsistent

How can you tell when a model doesn’t have stationarity?

1. there is a visible trend

2. The line clearly trends upward or downward over time (doesn’t stay flat).

3. when p-value is greater than 0.05

How can you tell when a model does have stationarity?

1. The plot looks like it “wiggles” around a flat horizontal line

2. when p-value is less than 0.05

3. doesn’t demonstrate a trend

What is a random walk?

A type of non-stationary time series process

The future value of the series is determined by its ___ value plus some random “___” or “error.

current; shock

How is a random walk inherently non-stationary?

The mean & variance of the series changes over time.

What is path dependence?

The future value depends entirely on the current value, making it difficult to predict beyond the short term.

What are the three key properties of a random walk?

No mean reversion, increasing variance over time, and no long-term predictable patterns

What is a good example of a random walk?

Stock prices

How do you transform a nonstationary series into a stationary one?

Using differencing: subtracting the previous observation from the current observation

What does differencing do as well?

Removes trends and makes the series stationary by stabilizing the mean.

If a visual does not display any consistency without trend, it is considered to be…

non-stationary

What is autocorrelation?

The correlation of a time series with its own past and future values.

What is the purpose of autocorrelation?

Identifies repeating patterns and relationships within data over time.

What is the difference between correlation and autocorrelation?

Correlation measures the relationship between two different variables where autocorrelation measures the relationship between different points in the same variable over time.

What does lag mean?

The time difference between the values being compared.

True/False: a lagged series with lag-1 is the original series moved forward one time period.

True

What does positive autocorrelation have?

High values follow high values, low will follow low

What does negative autocorrelation have?

High values follow low values, low follows high

What does “zero” autocorrelation have?

No predictable pattern between values

What is additive decomposition contribute to?

Seasonal variation stays roughly constant

What is multiplicative decomposition contribute to?

Seasonal variation increases with trend

What does a high alpha represent?

It is closer to 1; more weight is given to recent observations making the model more responsive to recent changes but also more sensitive to noise

What does a low alpha represent?

(closer to 0): More weight is given to older observations, resulting in a smoother series that is less responsive to recent changes (i.e., slow learning)

Why do we look at autocorrelation?

1. Detect seasonality

2. Help decide the parameters used in ARIMA model

3. Shows how far the past influences the future

Does the ACF plot alone tell you whether the trend is upward or downward?

No

Trend Data

The ACF plot for trend data typically shows a slow decay (values are correlated over long periods)

Seasonal Data

There are spikes at regular intervals corresponding to the seasonality period (negative autocorrelations in between these spikes) roughly every four months

What is level?

The baseline value for the series if it were a flat line

What is a trend?

The long-term progression of the series

What is seasonality?

Regular patterns or cycles repeating over time

What is noise?

Random variations in the series that do not follow any pattern

What is lag-1?

There is one time period difference between two data points

What steps are necessary to compute autocorrelation?

1. Create “lagged” series

2. Copy the original series, offset by one or more timer periods

3. Compute correlation between original series and lagged series, use the same cor() function

What is positive lag-1 autocorrelation?

Known as stickiness, its when the consecutive values move generally in the same direction.

True/False: If there is a strong linear trend, we would expect to see a strong and positive lag-1 autocorrelation

True

What is negative lag-1 autocorrelation?

Swings in the series, where high values are immediately followed by low values and vice versa

What is the ACF?

A statistical tool that measures the correlation between observations of a time series at different time lags.

The autocorrelation function starts a lag __, which is the correlation of the time series with itself and therefore results in a autocorrelation of _

0; 1

What is the ACF plot used for?

Used to identify significant lags in the data.

What are the dotted lines in the ACF plot?

Confidence bounds for judging statistical significance