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Lecture 24: Even more autoregression

Lecture 24: Even more autoregression. April 16, 2014. Question. Which of the following best describes your opinion about using “ clickers ” this semester: I found it useful and would suggest their use again They could have been useful but weren’t used well enough

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Lecture 24: Even more autoregression

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  1. Lecture 24:Even more autoregression April 16, 2014

  2. Question Which of the following best describes your opinion about using “clickers” this semester: • I found it useful and would suggest their use again • They could have been useful but weren’t used well enough • The idea is good but there are better ways/technologies • I did NOT find it useful and wouldn’t suggest any replacement • None of the above.

  3. Administrative • Clickers • Return Today or Monday (if you forgot yours today) • Exam 3 Monday • Will cover all forecasting methods through today • Example questions posted (for solutions, post your answers on Piazza – I’ll post an excel file this weekend). • Next Wednesday: Review + Bonus Quiz #2

  4. Last time • Non-stationarity • How do you visually check? • First (and higher) order differences • Transformation of the data • Hence you’ll need to transform it back to make it usable for a forecast.

  5. Quiz 5 • Results soon (hopefully) • Solutions posted. (both xls and pdf files)

  6. AR(p) models Recall the AR(p) regression model: Note that this still is only using the response data. • The data are sometimes called indistinguishable because the only thing we know about them is the temporal order of the Y • Most data that we might be interested in is distinguishable • We know how rate of Economic Growth in time t (and t-1, etc), but we also know the Inflation Rate at time t (and t-1, etc). • We have additional predictors that we could use to make a forecast of Yt.

  7. ADL models Most of the time we have a good theoretical reason to believe something other than Yt-1 might influence the value of Yt. ADL = Autoregressive Distributed Lag • Basically it’s the multiple regression version of AR models. • Now we can include other explanatory variables (X1, X2, etc.)

  8. ADL models Suppose you sell Land Cruisers (LCs) and want to determine the relationship between the number of inquiries received and the number of LCs sold in a given week. • Assume you record the number of inquiries you receive every week over the past year. • There’s probably some lag between the inquiry and whether someone buys the LC. Large purchases might take more than a week to inquire and then decide. • Hence we need to add a lag of the inquiry to a model of estimated LC sales.

  9. ADL models • Hence the ADL allows lags in all the variables. • Autoregressive: allow lags of the Response variable • Distributed Lag: because it allows multiple lags (different explanatory variables)

  10. ADL Assumptions • Essentially they’re the same as the MRM except • In the ADL stationarity in Y and all Xs (and all lags) is required. • Also essentially requires that autocorrelation goes to zero with sufficiently large time periods. • You can still fit an ADL if you violate these assumptions. As you can fit an MRM even if you violate the assumptions of the MRM. • But realize you’re violating the assumptions and use caution using the results.

  11. Previous Exam Questions Data: AAPL.xlsx • Estimate the following regression model: Predict closing price (PX_LAST) by lagged BEST_TARGET_PRICE, lagged BEST_EPS, and lagged BEST_ANALYST_RATING. Only lag by one period. What is the estimated model? Report the adjusted R2 and residual standard deviation. • Using this model, what is the estimated closing price of the stock on April 15th? Show at least two significant digits. • 461.27 • 465.34 • 429.80 • I have no idea

  12. Previous Exam Questions Data: AAPL.xlsx • From PX_LAST construct a stock returns variable, i.e., a percentage change in price: ΔYt / Y t-1. Estimate the following regression model to predict the stock return at time t by lagged BEST_TARGET_PRICE, lagged BEST_EPS, and lagged BEST_ANALYST_RATING. What is the estimated model? Report the R2 and RMSE. • Using this model, what is the estimated closing price of the stock on April 15th? Show at least two significant digits. • 431.28 • 445.34 • 429.49 • I have no idea

  13. Previous Exam Questions Data: AAPL.xlsx • Estimate an Autoregressive Distributed Lag (ADL) model predicting closing price by lagged PX_LAST, lagged BEST_TARGET_PRICE, lagged BEST_EPS, and lagged BEST_ANALYST_RATING. What is the estimated model? Report the adjusted R2 and residual standard deviation. • Using this model, what is the estimated closing price of the stock on April 15th? Show at least two significant digits. • 431.28 • 429.22 • 429.49 • I have no idea

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