Banca d Italia. Ministero dell Economia e delle Finanze. November Real time forecasts of in ation: the role of.

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1 Banca d Italia Ministero dell Economia e delle Finanze November 2008

2 We present a mixed to forecast in ation in real time It can be easily estimated on a daily basis using all the information available up to that date it combines the information on long-run and short-run dynamics of in ation Main ndings: it has a stronger predictive power than standard monthly s it outperforms forecasts implied in HICP-future contracts

3 Motivations Over the last few years there has been a growing importance in forecasting macro in real time: Monetary policy the introduction of explicit in ation targets the need of a modern monetary policy based on market expectations (Woodford 2003) Financial markets (and public debt management) anticipate Monetary Policy new contracts require continuous forecasts

4 Outline of the presentation We present the two main of our approach: ling the long run component of in ation daily Introduce mixed- data s Present our s for the EA HICP Two exercises of forecast evaluation to compare our s with standard s and market expectations

5 Modelling long run component with factor s Large dimensional Factor Models have become increasingly popular in the construction of reliable coincident and leading indicators Developed by Forni et al. (2000, 2005) and Stock and Watson (2002), they can handle in a parsimonious way the information contained in a large data set Factor det They do this by extracting few common components from the correlation structure of the data that explain most of the variability of the data 1 Examples of business index: EUROCOIN and Chicago Fed National Activity Index 2 Examples of core in ation: Kapetanios (2004) for UK and Cristadoro et al. (2008) for EA

6 Core In ation We use a Core in ation index obtained from a Generalized Dynamic Factor (Cristadoro et al. (2008)) This measure of core in ation is an estimate of the unobserved component that drives the persistent or long run movements in in ation By construction it is cleaned from the e ects of transient and idiosyncratic shocks: It is a smooth indicator It provides timely signal of future (long-medium run) price changes

7 COREINFL D12HICP

8 forecasting with factor s Large scale factor s are not ideal to forecast in real time: unbalanced end of sample temporal aggregation bias practical issues (download and data treatment) Flourishing of literature on these issues New Eurocoin (Altissimo et al. (2006)) Factor - MIDAS dealing with the end of sample adjustment (Marcellino-Schumacher (2008)) Mixed unobserved component s (Mittnik-Zadrozny (2005), Aruoba et al. (2007))

9 Role of An alternative solution is to look at that are highly correlated with in ation but that are sampled at higher, such as commodity prices and Notable characteristics of these : potentially forward looking released in continuous time not subject to revisions Use of to forecast in ation is not new. Stock and Watson (2001) present a good survey: evidence is not conclusive and results are dependent. Using DFM Forni et. al. (2003) and Giannone et. al. (2006) found some evidence

10 Our approach What we propose is a simple mixed that incorporates the previous approaches: 1 exploit the rich information on low-medium frequencies of in ation that comes from a Dynamic Factor Model 2 combine in a mixed the monthly core in ation index with daily prices of commodities and assets ) This allows us to capture recent information on possible movements of in ation as well as its long run underlying dynamics (no problems of unbalanced panel)

11 Mixed data s: Allows us to have in the same s sampled at di erent frequencies, e.g. monthly and daily They are particularly useful when the relevant explanatory come at high but the endogenous is sampled a lower We follow the speci cation of Mixed Data Sampling regression s (MIDAS) introduced by Ghysels, Santa-Clara and Valkanov (2004, 2007)

12 A simple MIDAS Let us assume the month t has M days, then a simple for monthly in ation π t is π m t = αzt m k L + βb M 1 ; θ + ε t = αzt m k + β M k=1 b (k; θ) L M k xt d + ε t = αzt m k b + β (1; θ) x d 1 + b (2; θ) x d ε t M t t M x d t z m t k is a vector of MONTHLY lagged ; x d t is the DAILY variable L M k is the daily lag operator: L M 1 xt d = x d 1 is the last daily observation of month t t M L 2 M x d t = x d t 2 M is the penultimate daily observation of month t

13 How to construct daily forecasts (1) Let asssume on 15 th of sept. I want to forecast current in ation. Estimate using monthly data til aug. and daily til the 4 th of sept. π aug = αz Jul + β 1 x d 14sept + β 2 x d 13sept + β 3 x d 12sept +... Forecast using the estimated parameter values ˆπ sept = ˆαz aug + ˆβ 1 x d 14sept + ˆβ 2 x d 13sept + ˆβ 3 x d 12sept +...

14 How to construct daily forecasts (2) Common speci cation for b (k, θ) are where f (k, θ) b (k, θ) = K k=0 f (k, θ) 1 f (k, θ) = exp θ 1 k + θ 2 k 2 ) Almon exponential pol. 2 f (x, θ) = Γ(θ 1+θ 2 ) Γ(θ 1 )Γ(θ 1 ) x θ 1 1 (1 x) θ 2 1 ) Beta pol.

15 Beta Function (shapes)

16 : 1 We compare three mixed s vs standard s 2 We compare them to in ation expectations extracted from HICP future contracts Dataset monthly/daily from May 1992 to September 2007 Estimation: iterative, constrained, nonlinear maximum likelihood Recursive forecast scheme

17 Three s for euro area (year-on-year HICP) in ation MONTHLY, common to all s: past in ation, lag of oil price and core in ation lagged ve Model 1: Captures shocks from both domestic and foreign prices: DAILY : the short term rate and changes in the interest rate spread and oil future prices Model 2: Captures shocks coming from abroad: DAILY var: changes in the wheat price, oil futures and exchange rate Model 3: Captures shocks only from interest rates: DAILY var: long term interest rate and changes in the interest rate spread and in the short term rate

18 monthly in ation First exercise we compute RMSFE of M1, M2 and M3 and compare them with those some benchmark s: AR and ARMA s chosen according to Schwarz criterion Two VARs including the same monthly as our s: this would tell us about the importance of daily We use 10 years as burning periods and generate recursive forecasts from May 2002 til Sept. 2007

19 Comparison with standard monthly s: RMSFE sample 2002:5-2007:9 months ahead Our s 0 1 Model Model Model Univariate s RW AR(1) ARMA(2,1) Multivariate s MV MV Note: MV 2: VAR with in ation, core in ation and oil price MV 3: VAR with in ation, core in ation, oil price and interest rate

20 : results All the mixed s outperform standard s In particular they produce better forecast than VARs showing that daily do improve forecasts The improvement compared to standard s is similar in t and t + 1 Among the mixed s MODEL 2 seem to produce the best forecasts

21 Model forecasts vs market expectations We compare our s forecasts with the current and one-month ahead expected in ation rate implied in quotes of EA HICP future daily contracts (CME) from October 2005 to September 2007 Why future contract underlying in ation rate: They are useful tool to extract market in ation expectations Wolfers and Gurkaynak (2006) predictive power of future contracts is better than that of survey data they also are better suited than the break-even in ation rate (negligible liquidity risk premium)

22 Daily forecasts (2005: :9) : chart current month 1.5 infla_d deriv M1 3/10/05 17/11/05 1/1/06 15/2/06 1/4/06 16/5/06 30/6/06 14/8/06 28/9/06 12/11/06 27/12/06 10/2/07 27/3/07 11/5/07 25/6/07 9/8/07

23 Daily forecasts (2005: :9) : box-plots Current month One month ahead Futures Model 1 Model 2 Model 3 Futures Model 1 Model 2 Mode

24 Comparison with daily futures: DM test Model (2.883) Model (2.277) Model (1.618) current month one month ahead squares abs squares abs (3.754) (3.061) (2.786) (0.763) (0.434) (0.943) (0.889) (1.748) (1.909) Note: Diebold Mariano test on the di erence between derivative and prediction errors. In parentheses, Newey West adjusted t-stat

25

26 Forecast combination RMSFE current month one month ahead single combined single combined Model Model Model Futures Note: Forecast combination with OLS estimated weights

27 : results Error distributions: smaller tails for the Mixed s outperform HICP-futures The improvement is statistically signi cant in nowcasting But the does not encompass the future prediction A forecast combination can reduce RMSFE by 5-10%

28 We presented an approach that: can be estimated and run daily to produce up-to-date forecasts combines the information on long-run and short-run movements of in ation performs quite well compared to standard s some room for improvement with market expectations

29 END OF PRESENTATION

30 How do they work? Let us assume a large number of time series y t = (y 1,t, y 2,t,..., y n,t ) Dynamic Factor Models extract a few common factors χ h,t, h = 1,...q such that y i,t = q b i,h (L) χ h,t + ξ i,t h=1 where ξ i,t is an idiosyncratic shock These common factors are chosen in order to explain most of the variability of the data at low and medium The common factors can be seen as the prediction of the common long-run dynamics of the data