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ucno "Is f IrXILI OI Nc ntOi F. '1,6 arin: Mihods: Ak overxiew of Be Bok 0 isl Booik, journals, Software, and Online Info rmation 6 :irse Probliems, aindi Compliemennts 9 r si in dail life: We are all forecasting, all the time 9 Fo reCC asing business, finance, economics, andc governmenit 9 Iwe imsic for cast.ing framework 10 D e>rees of forecastabilit: 10 ),t.i on thie wIeb io L jvariaCl amdl miilivariaei forecastinin models 10 i (-f-pts for Review t1 I >onees and Additional Readings 11 o. I, hI>1s Cd;l)apte U 13 M. oil \ldriables, Distributions, and Moments 14 Vu6irvawuae Randonl Viriables 15 L 4 s ies 16 5 , j e esyion. Alnaksis 18 ExeIcises, Problems, and Complernenits 30 Interpreting distributions and densities 30 Covariance and correlation 30 Conditional expectations versus linear projecions 30 Conditional mean and variance 30 Scatterplots and regression lines 30 Desired values of regression diagnostic statistics 3 Mechanics of fitting a linear regression 31 Regression wivth and with out a consta.nt teirm 3] Interpreting coefficienis and variables 31 Nonlinear least squares 31 Regression semantics 32 Bibliographical and Computational Notes 32 Concepts for Review 32 References and Additional Readings 33 i. The Decision Environment and Loss Function 35 2. The Forecast Object 39 3. The Forecast Statement 40 4. The Forecast Horizon 43 5. The Information Set 45 6. Methods and Complexity, the Parsimony Principle, and the Shrinkage Principle 46 71 Concluding Remarks 47 Exercises, Problems, and Complements 47 Data and forecast timing conventions 4.7 Properties of loss functions 47 Relationsh tips among point, in erial, and densitv forecasts i47 Forecasting at short through long ho.rizons 47 Forecasting as an ongoing process in organ-iza.tions 48 Assessing forecasting situations 48 Bibliographical and Computational Notes 49 Concepts for Review 49 References and Additional Readings 50 1. The Power of Statistical Graphics 51 2. Simple Graphical Techniques 55 3. Elements of Graphical Stvie 59 SApicat ion: Graphing Four ComponInClts of R0l GDP 63 , C hiucluing Remarks 66 E fr cise s, Problems, and Compeiements 67 Outliers 67 Siirple versus partial correlation 67 CAmmlcal regression diagnostic 1: time series plot 0of' V y. and e, 67 Graphical regression diagnostic 2: time sries plot of e or e, 68 Graphical regression diagnostic 3: scatierplot of e, versus ,R 68 Graphi cal an alysis of foreigrn exchange rate data 68 Commrnon scales 69 Gra:phin g real GDP. corlti imed from Section 4 69 Color 69 Regression, regression diagnostics. and regression graphics in action 69 Abli ogyraphical ,and Com pu tationAl Notes W7 Con.cepts for Review 71 Referenccs and Additional Readings 71 1. Modeling Trend 72 Es6i mating Trend Models 80 3 Fo' cast ing Trend 81 i S lectinl Forecasting Models Using the Akaie kk and Schwarz Criteria 82 5 Application: Forecasting Retail Sales 87 Ex cirses, ProblemCIs, anld CMrn plCDIents 94 Calculatlig forecasts from trend models 94 i1dendtivirn and testing- trend models 94 Un derstandmig model selection criteria 94 Mechanics of trend estimation andil forecasting 95 Properties of polynomial trelids 95 S'pecialized nonlinear trends 95 Moving average smw ooth ing for t end eistimation 95 Bias correcti ons when forecastng f roi logarithmic rnodels 96 odel selection for long-horizon forecalsting 97 The variety of i nformation teria" reported across software packages 97 Bibliographical an-d Co' putational .Notes 97 Concepts fbr Review 98 Referen cs anid Additiontial Realings 98 1 ithe Nature and Sources of Seasonalitv 99 2 MVodeling Scasonamlitv 101 3. Forecasting Seasonal Series 103 SApplication: Forecasting Housing Starts 104 Exercises, Problems, and Complements 108 Log transfobrmations in seasonal models 108 Seasonal adjustment 108 Selecting forecasting models involving calendar effects 108 Testing for seasonality 109 Seasonal regressiomns with an intercept and s - 1 seasonal dunmmies 109 Applied trend and seasonal modeling 109 Periodic models 09 Interpreting dummnn variables 110 Constructing seasonal models 110 Calendar effects 10 Bibliographical and Computational Notes 111 Concepts for Review 111 References and Additional Readings 1II Covaliance Stationary Time Series 113 2. White Noise 117 3. The Lag Operator 123 4. Wold's Theorem, the General Linear Process, and Rational Distributed Lags* 124 5. Estimation and Inference for the Mean, Autriocorrelation, and Partial Autocorrelation Functions 127 6. Application: Characterizing Canadian Employment Dynamics 130 Exercises, Problems, and Complements 132 Lag operator expressions 1 132 Lag operator expressions 2 133 Autocorrelation functions of covariance stationary series 133 Autocorrelation vs. partial autocorrelation 133 Conditional and unconditional means 133 White noise residuals 133 Selecti ng an employment forecasting model with the AIC and SIC 134 Simulation of a time series process 134 Sample autocorrelation functions for trending series 134 Sample autocorrelation functions for seasonal series 134 Volatility dynamics: correlogr'ams of squares 135 Bibliographical and Computational Notes 135 Concepts for Review 135 References and Additional Readings 136 1. Moving Average (MA) Models 138 2. Autoregrcssive (AR) Models 145 3. Autoregressive Mo\ing Average (ARMA) Models 152 Spplicon: Specif-ing and E.itimaring \Miodcls f5 PETmlmoment FOrecastin1 154 tEArcis; Problems, and Complements 163 ARMIA la, inchusion 16 Sh,apes of Tcorelograms 163 Me iutocoiVianice flunct"ion of th le MA ) proclss, revisited 163 .P I.'A aflgebra 163 D)aoic checking of miodel residuals 163 g - cheing of,: i Mechanics of fitting ARAŽL models 165 A-r(od(flng cyclical dynamics 165 A;gregadon and disnggregation: top-do-own forcasting model \s, botOin-li forecasting model 165 Nonlinear forecastinAg models: regiie switching 165 Difficulties with nonlinear optimihation 166 Bibliographical and Computational Notes 167 CoIn'epts for. Review 168 RcehPences a.nd Additional Readings 169 1, Optimal Forecasts 171 . Forecast ing Moving Average Pro esses 172 3. akaing tlhe Forecasts Operational 176 A I. Te C(.hain Rule of ForecastiIng 177 %5. 'piicati on: Forecastingr Ernlpovment ISO cxcrcJscs, Problems, and Complements 184 Oioecast accuracy across horizons 184 Mechanimcs of forecasting with ARi n-models: BankWire continued 184 Foi ecasinag an AR(1) process with known and unknowni pai:ameters 185 Foe ncasting an AR1LA(2, 2) process 185 0)ptimal forecasting under asymimetric loss 186 ni mCation of ilfinite distributed lags. state space representations, and the TKalnan ilter 18>7 Poin and interval forecasts ailowiig for serial correlation- Nile.comr continued 187 Bootstrapping simulation to acknowledge innovation :distribudion m ccrtainvi and parameter estimation iuncertaintv 188 IB ibliographlical ajnd Compulmional Notes 189 ConceDpts for Revicw Io) R.renr e s and Addi ti ona Readin gs 190 3. Recursive Estimation Procedures for Diagnosing and Selecting Forecasting Models 207 4. Liquor Sales, Continued 212 Exercises, Problems, and Complemenrs 214 Serially correlated disturbances vs. lagged dependent variables 214 Assessing the adequacy of the liquor sales forecasting model trend specification 214 Iipn roving nontrend aspects of the liquor sales forecasting model 21-1 CITSUM analysis of the housing starts model 215 Model selection based on simulated foriecasting performance 215 Seasonal models with time-varNying parametes f0orecasting AirSpeed passenger-m4iles 215 ForLmal models of unobserved components 216 T'he restrictions associated with unobserved-components structures 216 Additive unobserved-components decomposition and rmuliplicatirve unobserved-conpmonents decompositon 21>7 Signal, noise, and overfitting 237 Bibliographical and Coinputational Notes 217 Concepts for Review 218 References and Additional Readings 218 i. Condiional Forecasung Models and Scenario Analysis 220 A.-co-ni -ting for Parant'ser Uncertainty in Confidence Snterva1s for Conditional F'o ecasts 22 0 3. Unconditional Forecasting Models 223 4 Distributed ILags, Polynomial Distributed Lags, and Rational Distributed Lags 224 5. Regressions with Lagged DCpendent Variables, Regressions with A.RMA Disturbances, and Transfer Function Models 225 6. Vector Autoregressions 228 7. Predictive Causality 230 8. Impulse-Response Functions aid Variance Deconmpositions 231 9. Application: Housing Starts and Completions 235 Exercises, Problems, and Comiplenents 249 Econometrics, time series analysis, and forecastring 249 Forecasting crop vields 249 Regression forecasting models with expectations, or anticipatory, data 249 Business cycle analysis and forecasting: expansions, contractions, turning points, and leading indicators 250 Subjective information, Bayesian VARs, and the Minnesota prio 251 Housing starts and comipletions, continued 251 Nonlinear regression models 1: functional form arid Ramsev's test 251 Nonliinear regression models 2: logarithmrnic regression models 252 Nonlinear regression models 3: neural networks 252 Spurious regression 253 Comparative forecasting performance of VAR and univariate models 254 b Bibliog3pic al a md Com(putational Notes 2A C-o;- ncepts ftor Rev\iw 255 lRZtrences and Adcitionial Redings 255 n Evahiatdng a Single Farnc as 257 SEvluah:tig Ivtwo or More Forecasts: Comparing Forec,ast Accuracy 260 A. flucast Enicomnpaissing and FTr'ncast nbinatdon 263 4. ication: OveuS Cea Shipping No,luime on the thntic East Trade Lane 26 Exercises, Probienis, and Compllements 280 For:ecast evaluation in action 280 Forecast erro analysis 280 CoTni:-ning forecasts 280S uanf ti\tt e foreaisting , idgmental t forecasti ig, recast combination, and dshrinkage 281 The algebra of Forecast conb in ation 2 The m1echanics pracical Torecast evaluation and (omb ination 282 \Ahat are we tforecastin T rPi imina s isd seris, 2and i limits o trecat accunny 289 Ex post versus real-time fiorecas evluavion 2 Whal do h i know about the accuracy of rmactoeconiom rni forcast? 283 For ccas evluation when realizions are unobservcd 283 irecast error vari a ces in models w ih est imatcd param ers 283 fhe ernpirim stcess of forcais comn xfi ntion 284 Fcwrecast curinatiot :mnd the BoxjenAkiN payndinjim 284 Consn'sus forecasts, 285 Ablingraphijcal and Comput,itonal Nos 2S5 Conc p ts for Review 286 RAfmences and Additional Readu 86 1. Stockisth Trcid, an0d Forec tingl 8 2. Unit R-oti: Ei:niation an:s TAesty. 2 3. Applicaon: Mode ng nd Forecing Dollar L chan e- Ra 30 SSmoothing 312 5. ELxchmn,e Rates, Ccmitmndl 318 SExercis.s. PrWo le.mni, and Compeint 320C ModI eling and rctsting tie iot ec e oiad ( iDEM, LSD) exchangc iat 320 >Crx B P . Uyarinc 0 ( i &0 O' i t/ NFi.Fis 14I Housing starts and completions, continued 320 AREJMA models, smoothers, and shrinkage 320 Using stochastic trend unobserved-components models to impireenit smnioothing techniques in a probabilistic framework 320 Auitomnatic ARIMA m rleling 321 The multiplicative seasonal ARIA (p, (d, q) x (P, A1, Q) model 321 The Dickev-Fuller regrpession in the AR () case 321 lHolWinters smoonhing with multiplicative seasonality 322 Cointegration 323 Error correction 323 Forecast encompassing tests for 1(1) series 324 Evaluating forecasts of integrated series 324 Theis Ustatistic 324 Bibliographical and Computational Notes 325 Concepts for Review 326 Refer ences and Additional Readings 326 1. The Basic AR.CH Process 330 2. The GARCH Process 333 3. Extensions of ARCH anid GARCH Models 337 4. Estirnating. Forecasting, and Diagnosing GARCIH Models 340 SApplication: Stock Market Volatility 341 Exercises, Problems, an d Complements 349 Removing conditional mean dynamics before modeling volatilitv dynamics 349 "Variations on the basic ARCH and GARCH models 349 Empirical performance of pure ARCH models as approximations to volatilitv dynamics 349 Direct modeling of volaility proxies 350 GARCH volatility forecasting 350 Assessing volatility dynamics in observed returns and in standardized returns 350 Allowinig for leptokurtic conditional densities 351 Optimnal prediction under asymmetric loss 351 Midtivariate GARC1H models 351 Bibliographical and Computational Notes 352 Concepts for Review 352 References and Auditional Readings 353