Lecture ElevenOutlineOutlineMemory LanePowerPoint PresentationSlide 6Slide 7Memory laneSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Outline-SummaryProcessProcess for Pre-whitened SeriesProcess: EstimationForecasting with an acceptable modelSlide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Economic ApplicationSlide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Term StructureSlide 62QuestionsSlide 64Slide 65Slide 66Slide 67Slide 68Conclusion About Term StructureSlide 70Slide 71Slide 72Slide 731Lecture ElevenEcon 240C2Outline •Review•Stochastic Time Series–White noise–Random walk –ARONE: –ARTWO–ARTHREE–ARMA(2,2)–MAONE*SMATWELVE3Outline•Forecasting–Federal: Federal Reserve @ Philidelphia–State: CA Department of Finance–Local•UCSB: tri-counties•Chapman College: Orange County•UCLA: National, CA4Memory Lane•White Noise = wn(t)5Nov 14, 2003April 29,2005678Memory lane•Random walk = [1 – z]-1 wn(t)9Weekly Closing Price of Gold29-Apr-05Nov. 14, 200334036038040042044046014710131619222528313437404346495255586164677073Date$ per oz.10111213Memory Lane•ARONE = [1 – bz]-1 wn(t)•ARONE = [1 – 0.62z]-1 wn(t)141516•Realchpvti(t) – 21.8 = Res(t)•Res (t) = [1 – 0.62z]-1 wn(t)•Realchpvti(t) – 21.8 = [1 – 0.62z]-1 wn(t)•Realchpvti(t) – 21.8 = .62[Realchpvti(t-1) – 21.8] + wn(t)•Realchpvti(t) – 21.8 = .62*62[Realchpvti(t-2) – 21.8] + wn(t) + 0.62wn(t-1)171819Memory Lane•ARTWO = [1- b1 z – b2 z2 ]-1 wn(t)•dstarts = [1- 0.45 z – 0.21 z2 ]-1 wn(t)•[dstarts – 3.24] = [1- 0.45 z – 0.21 z2 ]-1 wn(t)20212223Memory Lane•ARTHREE = [1- b1 z – b2 z2 – b3 z3 ]-1 wn(t)•Dlnffr(t) = [1- 0.148z2 – 0.135z3 ]-1 wn(t)–Constant is insignificantly different from zero24252627Memory Lane•ARMA(2,2) = [1 + a1 z + a2 z2 ]*[1 – b1 z –b2 z2 ] wn(t)•[ Starts – 1110.4] = [1 – 0.178 z2][1 – 0.653z – 0.319z2]-1 wn(t)2829Memory Lane•(1-z)(1-z12) ln bjpass(t) = MAONE*SMATWELVE•(1-z)(1-z12) ln bjpass(t) = (1 –a1 z)(1 – a12 z12) wn(t)•(1-z)(1-z12) ln bjpass(t) = (1 –0.377 z)(1 – 0.624 z12) wn(t)–Constant not significantly different from zero303132010020030040050060070049 50 51 52 53 54 55 56 57 58 59 60 61BJPASS BJPASSFTwelve Month forward Forecast of Airline Passengers33Outline-Summary •Review•Stochastic Time Series–White noise–Random walk: weekly price of gold–ARONE: real change in private inventories, quarterly–ARTWO: monthly change in private housing starts, single units–ARTHREE: monthly fractional change in federal funds rate–ARMA(2,2): private housing starts, single structures, monthly–MAONE*SMATWELVE: airline passengers, monthly•All data from Fred except price of gold, airline passengers–Freddy, we hardly knew ye34Process•Identification–Spreadsheet•Any funny numbers?–Plot (trace)•Any time dependence? –Trend in variance?–Trend in mean?–Seasonality?•If so, prewhiten–Log transform–First difference–Seasonal difference35Process for Pre-whitened Series•Identification–Spreadsheet•Are transformations correct?–Plot•Is it close to white noise?–Histogram•Is it single peaked?–Correlogram•Is there a small amount of prominent structure?•PACF: order of AR terms•ACF: order of MA terms•Postulate alternative ARMA models–Augmented Dickey-Fuller tests•Is it stationary?36Process: Estimation•Estimate a trial ARMA model–Are the estimated parameters significant?–Record ser•Validation–Actual, fitted, residual: •Does the model fit the data?•Do the residuals look white?–Correlogram of the residuals•Are they orthogonal? If not, modify the model–Histogram of the residuals•Are they normal?37Forecasting with an acceptable model•Hand calculate a one period ahead forecast•Estimate the model, leaving some data to check the forecast•Forecast for the test period using competing models•Plot the series, its forecast, and ~ 95% confidence interval•Recolor if necessary–Could show fractional changes, forecast, upper, lower–Also original series, forecast, upper*, lower*•* exponentiated upper and lower from above38Outline•Forecasting–Federal: Federal Reserve @ Philidelphia–State: CA Department of Finance–Local•UCSB: tri-counties•Chapman College: Orange County•UCLA: National, CA3940http://www.phil.frb.org/files/spf/survq105.html41424344http://www.dof.ca.gov/4546474849505152Economic Application•The Term Structure of Interest Rates535455565758The big gap596061Term Structure•Ratio = treas20yr/bill3mth6263Questions•Did the Fed drive short-term interest rates down?•Did the Fed drive long-term interest rates down, and create a bubble in housing prices?646566676869Conclusion About Term Structure•The federal funds rate is affecting the 3 month bill rate and vice versa•The federal funds rate is not affecting the 20 year bond
View Full Document
Unlocking...