Time Series Analysis
Routing Summary
ARIMA, transfer functions, VAR, cointegration, ECM, and Granger causality for marketing time series.
- Stationarity, ARMA, ARIMA, ACF/PACF, Box-Jenkins → Single Marketing Time Series
- Transfer function model, prewhitening, intervention analysis → Transfer Function Model
- VAR, impulse response, cointegration, ECM, 4 strategic scenarios → Multivariate Persistence and Cointegration
- Granger causality, IRF, FEVD, Cholesky ordering → Empirical Causal Ordering
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| Univariate ARIMA / Box-Jenkins | Single Marketing Time Series | concept | Markets Data and Sales Drivers, Carryover Effects and Distributed Lags, Design of Dynamic Response Models | Box-Jenkins ARIMA characterizes univariate marketing series structure |
| Transfer function models | Transfer Function Model | concept | Single Marketing Time Series, Carryover Effects and Distributed Lags, Design of Dynamic Response Models | Relates marketing output to inputs with autocorrelated noise |
| Persistence & cointegration | Multivariate Persistence and Cointegration | concept | Transfer Function Model, Single Marketing Time Series, Reaction Functions and Competitive Dynamics | VAR captures six channels; cointegration tests long-run equilibrium |
| Empirical causal ordering | Empirical Causal Ordering | concept | Multivariate Persistence and Cointegration, Reaction Functions and Competitive Dynamics | VAR causal ordering via Granger tests, impulse responses, variance decomposition |
Notes
- Single Marketing Time Series — CONTAINS: weak/covariance stationarity (Eqs 6.5-6.6), deterministic components (trend, seasonality, cyclicality, heteroscedasticity), linear-filter representation (Eq 6.10), ARMA (Eq 6.11), ACF (Eq 6.27) and PACF, AR(1) (Eqs 6.40, 6.42) and MA(1) models, the ACF/PACF diagnostic summary (Table 6-2), the Box-Jenkins identification procedure, ARIMA(p,d,q) (Eq 6.76), seasonal ARIMA (Eq 6.79), and Box-Cox variance stabilization (Eq 6.74).
- Transfer Function Model — CONTAINS: single-input transfer function (Eqs 7.7-7.8), two-input TF model (Eqs 7.14-7.15), prewhitening identification (Eqs 7.9-7.12), cross-correlation function (CCF) patterns, Liu-Hanssens (1982) direct-lag regression (Eq 7.16), intervention analysis (Box-Tiao 1975, Eqs 7.19-7.20), pulse and step interventions with response scenarios, and residual ACF/CCF diagnostic checking.
- Multivariate Persistence and Cointegration — CONTAINS: VARMA (Eq 7.21), VAR (Eq 7.22), bivariate sales-advertising VAR (Eq 7.23), the six channels of total impact (Dekimpe & Hanssens 1995a), multivariate persistence (Eq 7.24), four strategic scenarios (business-as-usual, escalation, hysteresis, co-evolution), cointegration (Engle-Granger 1987, Eq 7.26), Engle-Granger and Johansen FIML tests (Eqs 7.27-7.28), and the error-correction model (ECM, Eq 7.29).
- Empirical Causal Ordering — CONTAINS: Granger causality tests (F-test, likelihood ratio), impulse response function (IRF), forecast error variance decomposition (FEVD), Cholesky (triangular) decomposition, structural VAR (SVAR), the Evans-Wells (1983) method, and short-interval-data causal ordering (advertising → price → sales).