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Empirical Methods for Finance 2 > Non-Stationarity and Volatility > Flashcards

Non-Stationarity and Volatility Flashcards

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1
Q

What is a stationary time series?

A

A series where mean, variance, and autocorrelation remain constant over time.

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2
Q

Why is non-stationarity a problem in regression?

A

It leads to biased estimates, spurious results, and unreliable forecasts.

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3
Q

What is a stochastic trend?

A

A trend driven by random shocks that accumulate over time, making it unpredictable.

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4
Q

What is a deterministic trend and how to remove it?

A

A predictable trend driven by time, removable by including time as a variable.

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5
Q

What are two forms of non-stationarity?

A

Stochastic trend and deterministic trend

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6
Q

What is a random walk?

A

A series where each value equals the previous value plus a random shock.

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7
Q

How do you make a random walk stationary?

A

By differencing to Delta Y

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8
Q

What is the difference between stochastic and deterministic trends?

A

Stochastic trends are driven by shocks and unpredictable; deterministic trends are predictable and linear.

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9
Q

What is unit root?

A

A property of a non-stationary series where shocks persist indefinitely.

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10
Q

What tests are used for stationarity?

A

Dickey-Fuller Test; tests H0: Non-stationarity
KPSS Test; vice versa.

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11
Q

What does I (1) mean?

A

The series becomes stationary after the first differencing.

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12
Q

What are the advantages of differencing to address non-stationarity?

A

Removes stochastic trends, converts non-stationary series to stationary and it simplifies modeling.

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13
Q

What are the disadvantages of differencing?

A

Can remove meaningful long-term information.
Over-differencing can lead to unnecessary loss of data patterns.

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14
Q

What is spurious regression?

A

A misleadingly high correlation between unrelated non-stationary variables.

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15
Q

How do you detect spurious regression?

A

Check if variables are stationary

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16
Q

Why do financial time series often exhibit stochastic trends?

A

Variables like stock prices or exchange rates reflect accumulated market shocks and have persistent trends.

17
Q

What are advantages of testing for unit roots?

A

Identifies non-stationary processes and it determines if differencing is required.

18
Q

What are the disadvantages of unit root tests?

A

Small sample sizes can yield ambiguous results and near-unit-root processes can mimic true unit roots.

19
Q

What are the two main stylized facts about volatility?

A

Volatility clustering: high volatility periods follow each other
Leverage effect: volatility increases when prices fall

20
Q

What is historical volatility?

A

The standard deviation or variance of returns over a historical period.

21
Q

What are the advantages of historical volatility?

A

Easy to calculate and provides a benchmark for other models.

22
Q

What are the disadvantages of historical volatility?

A

Does not account for volatility clustering, and treats all observations equally, ignoring recency.

23
Q

What is the rolling window approach?

A

A method that calculates volatility using only the most recent data in a fixed period.

24
Q

What is the advantage of the rolling window method?

A

Captures short-term changes in volatility.

25
Q

What is the disadvantage of the rolling window method?

A

Disregards older data that might still hold valuable information.

26
Q

What is EWMA?

A

The Exponentially Weighted Moving Average assigns higher weights to recent returns, using a decay factor lambda.

27
Q

What is the advantage for EWMA?

A

Captures volatility clustering effectively, gives more importance to recent observations.

28
Q

What is the disadvantage of EWMA?

A

Assumes fixed decay (lambda) which may not adapt to market shifts.

29
Q

What does ARCH stand for?

A

Autoregressive Conditional Heteroskedasticity

30
Q

What does the ARCH model do?

A

Models conditional variance as a function of past squared returns.

31
Q

What are the advantages of ARCH models?

A

Captures volatility clustering and provides a structural way to model time-varying volatility.

32
Q

What are the disadvantages of ARCH models?

A

Choosing the lag length can be difficult
Prone to overfitting with high Q
May violate non-negativity constraints

33
Q

How is GARCH different from ARCH?

A

GARCH includes lagged variances in the model, making it more flexible.

34
Q

What are advantages of GARCH models?

A

More parsimonious than ARCH
Avoids overfitting
Captures both short and long term volatility patterns

35
Q

What are the disadvantages of GARCH?

A

More complex to estimate and may not capture non-linear effects well

Empirical Methods for Finance 2 (6 decks)

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