I am trying to estimate a Macroeconomic VAR/BVAR for the purpose of forecasting/impulse response simulations.   I have a total of 5 macro variables that are 4 country specific and 1 for the Euro Area : GDP_BG - GDP ; HICP_BG - Inflation; HP_BG - House prices ; Unemp_BG - Unemployment ; GDP_EA - GDP euro area   I have colelcted quarterly and monthly data for the period 2006 - 2016. After cubic interpolation of the quarterly data all series are in monthly year on year grwoth format.   1. DF tests indicate non-stationarity of the series: Dickey-Fuller Unit Root Tests Variable Type Rho Pr < Rho Tau Pr < Tau GDP_BG Zero Mean -8.62 0.0402 -1.95 0.0495   Single Mean -15.03 0.0348 -2.64 0.0885   Trend -17.17 0.108 -2.93 0.1564 GDP_EA Zero Mean -42.7 <.0001 -4.44 <.0001   Single Mean -48.69 0.0011 -4.75 0.0002   Trend -48.02 0.0004 -4.73 0.001 Unemp_BG Zero Mean -0.18 0.6399 -0.22 0.6043   Single Mean -5.76 0.36 -1.77 0.3947   Trend -7.8 0.5888 -2.33 0.4161 HICP_BG Zero Mean -1.13 0.4495 -0.48 0.5071   Single Mean -3.39 0.6051 -1.18 0.6833   Trend -12.61 0.2665 -2.51 0.3215 HP_BG Zero Mean -13.83 0.0087 -2.61 0.0093   Single Mean -14 0.0458 -2.61 0.0929   Trend -14.24 0.1953 -2.74 0.2225 2. Taking this into account I run the VAR(3) - suggested by the minimum information criteria   /* VAR with 1st Difference*/ proc varmax data=DATA_ALL.MACRO_CLEAN_ALL; model GDP_BG GDP_EA Unemp_BG HICP_BG HP_BG / p=3 noint dftest dify=(1) print=(estimates); run;   3. The DF test now indicates stationarity, however, there is no significant relationship apart from the diagonal elements of the AR parameters, except for higher order lags:   AR Coefficient Estimates Lag Variable GDP_BG GDP_EA Unemp_BG HICP_BG HP_BG 1 GDP_BG 1.51695 -0.32323 -0.07316 0.0208 0.04657   GDP_EA 0.04184 1.54188 -0.0317 -0.00889 0.02111   Unemp_BG 0.0585 -0.13691 1.01772 0.02646 -0.01353   HICP_BG -0.09687 -0.17317 0.45338 0.26286 0.05087   HP_BG 0.40168 -0.6717 -0.16238 0.07366 1.52713 2 GDP_BG -1.24578 0.57102 0.24424 -0.007 -0.01004   GDP_EA -0.01199 -1.08216 0.046 -0.00174 -0.01859   Unemp_BG -0.03327 0.1483 -0.32875 -0.02099 0.01321   HICP_BG 0.02011 1.41164 -0.48313 -0.00346 -0.11958   HP_BG -0.27895 2.18608 -0.45604 0.22938 -1.32891 3 GDP_BG 0.4411 -0.33352 -0.25461 -0.04826 0.01708   GDP_EA 0.02513 0.38162 -0.01667 -0.01701 0.01481   Unemp_BG -0.02864 0.10291 -0.01005 -0.03522 0.00014   HICP_BG 0.31382 -1.4971 -0.1214 0.14482 0.10065   HP_BG 0.35618 -2.09016 0.63977 0.11498 0.54739               Schematic Representation of Parameter Estimates       Variable/Lag AR1 AR2 AR3       GDP_BG +.... -.... +....       GDP_EA .+... .-... .+...       Unemp_BG ..+.. ..-.. .....       HICP_BG ...+. ..... .-...       HP_BG ....+ ...+- .-..+       + is > 2*std error,  - is < -2*std error,  . is between,  * is N/A         If I proceed with imposing a BVAR prior the  higher order lags are eliminated by the prior and the resulting model has significant parameters at low order diagonal parameters.   I don't understand the reason for these results. How is it possible that stationary macro variables do not have any dependence between each other? Any suggestions for what am I making wrong and what could I try?   Could the monthly frequency be the reason for these results? If so should I test much higher lag orders (p=12) and then restrict the insgignificant parameters? ... View more