







































DYNAMIC ECONOMETRIC MODELS 
Vol. 11 – Nicolaus Copernicus University – Toruń – 2011 

Mariola Piłatowska  
Nicolaus Copernicus University in Toruń  

Information and Prediction Criteria in Selecting  
the Forecasting Model 

A b s t r a c t. The purpose of the paper it to compare the performance of both information and 
prediction criteria in selecting the forecasting model on empirical data for Poland when the data 
generating model is unknown. The attention will especially focus on the evolution of information 
criteria (AIC, BIC) and accumulated prediction error (APE) for increasing sample sizes and roll-
ing windows of different size, and also the impact of initial sample and rolling window sizes on 
the selection of forecasting model. The best forecasting model will be chosen from the set includ-
ing three models: autoregressive model, AR (with or without a deterministic trend), ARIMA 
model and random walk (RW) model. 

K e y w o r d s: information and prediction criteria, accumulated prediction error, model selection. 

Introduction 

 The model selection literature has recently emphasized the necessity of con-
sidering the choice of model depending on the purpose of econometric model-
ing. In modeling approach the two aims are mentioned the most frequently, 
namely searching 'true' model and selecting the best forecasting model (optimiz-
ing prediction).  

 That first aim of modeling is hard to realize because  the economic reality is 
seen as a complex and dynamically evolving structure whose mechanism is 
hidden and almost impossible to uncover. Therefore the model is an approxima-
tion (or simplification) of reality which represents the relevance of a particular 
phenomenon. It is advocated to assume that each model is not true by definition 
(Taub, 1993; deLeew, 1998) or that "all models are wrong, but some are useful" 
(Box, 1976). Having in mind that none of models cannot reflect all of reality, 
the debate concerning true models should be completed because it seems to be 
unproductive. Hence, the second aim of modeling, i.e. selecting the best fore-
casting model acquires relevance from the practical point of view. 



Mariola Piłatowska 22

 In predictive approach the goal of selecting the true model is abandoned and 
the attention focuses on seeking a model with as small predictive errors as pos-
sible. It should be emphasized that in forecasting situation the misspecified 
model are allowed because such a model may yield excellent forecasts. On the 
other hand good prediction is treated as a test of any subsidiary aim, i.e. if the 
purpose of an analysis is to estimate parameters, then the best estimated model 
should give the best prediction; if the purpose of an analysis is hypothesis test-
ing, then any rejected model should give worse forecasts than any accepted 
model (Clarke, 2001; De Luna, Skouras, 2003; Kunst, 2003). 

 To select the forecasting model the different model selection methods can 
be used, for instance information and prediction criteria. However, question 
may arise whether the performance of both criteria is the same with regard to 
the choice of model. It has been shown on simulated data1 (Kunst, 2003) that 
information criteria should be rather used if one is interested in finding 'true' 
model. If the purpose of analysis is to choose a forecasting model, the predic-
tion criteria are preferred because they select the model yielding the smallest 
prediction error, although sometimes it may be an incorrect choice (not true 
model). However, in economic reality the true model is unknown, therefore it is 
worth checking the performance of information and predictiion criteria in prac-
tical context (empirical data).  

 The purpose of the paper it to compare the performance of both information 
and prediction criteria in selecting the forecasting model on empirical data when 
the data generating model is unknown. The attention will especially focus on 
the evolution of information criteria (AIC, BIC) and accumulated prediction 
error (APE) for increasing sample sizes and rolling windows of different size, 
and also the impact of sample and rolling window sizes on the selection of fore-
casting model. The best forecasting model will be chosen from the set including 
three models: autoregressive model, AR (with or without a deterministic trend), 
ARIMA model and random walk (RW) model on the basis of empirical data for 
Poland. The choice of model will be carried out using information (AIC, BIC) 
and prediction (APE and MSE, MAPE, U) criteria. The decision of selecting 
a model by information and prediction criteria is checked in out-of-sample fore-
casting by comparing accuracy measures for given forecast models. 

                                                 
1 The true data were generated from ARMA(1, 1) models with 100+100+10 observations 

(first 100 observations were discarded; 1000 replication were conducted). The set of models 
included: ARMA(1, 1), AR(1) and MA(1) models. To select a model the AIC information criteri-
on and the mean squared error (MSE) based on prediction error from 10 one-step-ahead forecasts 
were applied (see Kunst, 2003).     



Information and Prediction Criteria in Selecting the Forecasting Model  23

1. Information and Prediction Criteria  

 Generally, information criterion takes the form:  

,)ˆ(ln2 qLIC    

where )ˆ(L  is the likelihood function, and q is a penalty term that is a function 
of the number of parameters K and the number of observations n; this penalty 
guards against overfitting, i.e. using too many parameters. For Akaike's infor-
mation criterion (AIC) the penalty is equal to ,2Kq   for Schwartz (Bayes) 

information criterion − ),ln(nKq   for Hannan-Quinn information criterion  − 
).ln(ln2 nKq    

For small samples the AIC criterion is biased and may suggest a model with 
a high number of parameters compared with the number of observations 

).40/( Kn Thus a bias-corrected version, AICc, is increasingly used. The latter 

is given by adding the quantity  )1/()1(2  KnKK  to the ordinary AIC. The 
BIC (like the AICc criterion) penalizes the addition of extra parameters more 
severely than the AIC, and should be preferred to the ordinary AIC in time-
series analysis especially when the number of parameters is high compared with 
the number of observations.  

 Applying information criteria in model selection the model with the mini-
mum of a given information criterion is chosen.   

 To traditional prediction criteria, used both in the accuracy evaluation and 
selection of forecasting model, belong:  

Mean Absolute Error ,
||

1

T

e
MAE

T

t t   

Mean Square Error ,1
2

T

e
MSE

T

t t   

Root Mean Square Error ,MSERMSE   

Mean Absolute Percentage Error %,100
|/|

1

T

ye
MAPE t

T

t t   

Theil's Inequality Coefficient ,
model)benchmark''(

)modelnew''(

RMSE

RMSE
U   

where te  denotes prediction error, ,ˆttt yye   ty  − realization of y  in period 

t, tŷ  − forecast of y  for period t.    

 Applying usual accuracy measures the model with the smallest value of 
given measure is selected what corresponds to the smallest prediction error.   



Mariola Piłatowska 24

 The Theil's inequality coefficient U indicates whether a given model is 
worse (U > 1) or better (U < 1) than the random walk model ( tt yy 1ˆ ) consid-
ered as a benchmark model.  

 It is worth highlighting that the choice of accuracy measure can affect the 
ranking of forecasting methods, and also models (Armstrong, 2001; Armstrong, 
Fildes, 1995). For instance, the MSE depends on the scale in which the variable 
is measured. This means that the MSE is appropriate only for assessing the re-
sults for a single time series, and should be avoided to assess accuracy across 
(many) different series. In that case the scale-independent measures are re-
quired2, e.g. MAPE or Theil's inequality coefficient (U). Besides, for the reason 
that the loss function may be asymmetric (e.g. underforecasting is worse than 
overforecasting), it may be important to forecast the direction of movement or 
to predict large movements (Chatfield, 2000). However, it is not possible to 
select a measure of forecast accuracy that is scale-independent and yet satisfies 
the demands of the appropriate loss function. In conclusion, there is no measure 
suitable for all types of data and all contexts. There are many empirical evi-
dence that a method which is 'best' under one criterion need not be 'best' under 
alternative criteria (e.g. Swanson and White, 1997).     

 The choice of forecasting model may also be carried out by the accumulated 
prediction error, APE, (Rissanen, 1986). According to the APE the most useful 
model is the model with the smallest out-of-sample one-step-ahead prediction 
error. 

 The APE method proceeds by calculating sequential one-step-ahead fore-
casts based on gradually increasing sample. For model Mj the APE is calculated 
as follows (Wagenmaker, Grünwald, Steyvers, 2006):  

1. Determine the smallest number s of observations that makes the model 
identifiable. Set ,1 si  so that .1 si   

2. Based on the first 1i  observations, calculate a prediction ip̂  for the next 

observation .i  

3. Calculate the prediction error for observation i, e.g. squared difference be-
tween the predicted value ip̂  and the observed value .ix   

4. Increase i  by 1 and repeat steps 2 and 3 until .ni   

5. Sum all of the one-step-ahead prediction errors as calculated in step 3. The 
result is the APE.   

For model jM  the accumulated prediction error is given by:  

)],ˆ(,[)( 11  ii
n

si ij xpxdMAPE  

                                                 
2 Mentzer and Kahn (1995) found in a survey of 207 forecasting executives in US that MAPE 

was the most commonly used measure (52%) while only 10% used MSE.   



Information and Prediction Criteria in Selecting the Forecasting Model  25

where d  indicates the specific loss function that quantifies the discrepancy 
between observed and predicted values. 

 In the case of point predictions one typically uses the squared error 
2)ˆ( ii px  , but another choice would be to compute the absolute value loss   

ii px ˆ , or more generally, an α-loss function, 


ii px ˆ , ]2,1[   

(Rissanen, 2003).   

2. Selection of Forecasting Model – Empirical Examples 

 To compare the performance of information and prediction criteria in select-
ing the best forecasting model the monthly data on consumer price index CPI 
(corresponding period of previous year =100) and industry production IP  
(in billion PLN zl) in Poland were used3 (in the period 2002:01−2010:12, 108 
observations, data are seasonally adjusted). The reason for such selection of 
time series is the desire to check the performance of selection criteria with re-
gard to time series of different properties, i.e. in the above case CPI is expected 
to be rather an integrated process, and IP − rather a stationary process around 
deterministic trend4.   

 The set of candidate models for CPI includes: autoregressive model, 
AR(12), ARIMA(12,1,0) model and random walk model (RW) as a benchmark 
model; for industry production IP this set was as follows: linear trend model 
with autoregression of twelfth order (further denoted as AR for the convenience 
of presentation), ARIMA(12,1,0) and random walk model as a benchmark  
model5.  

Two versions of estimation procedures are considered: 

version I: the models are iteratively estimated beginning with the initial sample 
size n(s) which is being increased by one until n = 108 (until 2010:12); three 
sizes of initial sample n(s) are taken: 40, 60, 80;  

version II: the models are iteratively estimated for rolling window size of 40, 
60 and 80 observations.  

The question is to what extent the size of initial sample and rolling window 
have the impact on the choice of forecast model when the information criteria 

                                                 
3 Data have been taken from the Statistical Bulletin of the Central Statistical Office in Poland.  
4 Many empirical studies conclude that the consumer price index (CPI) as a financial series is 

rather integrated and then the ARIMA model is more appropriate than the AR model (with or 
without deterministic trend). Whereas, the industry production (IP) is treated rather as a stationary 
process around deterministic trend and then the AR model (with or without deterministic trend) is 
often taken as a more correct model.  However, it may occur in forecasting that an inappropriate 
model  will yield better forecasts. To take into account this possibility, both models are used in 
empirical study. 

5 The order of autoregression was fixed at 12 as the potentially highest order reflecting 
monthly frequency of data.  



Mariola Piłatowska 26

(AIC, BIC) and prediction criteria (APE_SE, APE_AE) are used as selection 
criteria. Notations APE_SE and APE_AE denote the accumulated prediction 
error (APE) that uses the squared error and absolute error respectively as a loss 
function.  

 To make a choice of best forecasting model the information criteria (AIC 
and BIC) and prediction criteria (APE_SE and APE_AE) were calculated at 
each iteration. The results are presented in Figures 1−8 as difference in a given 
criterion for pairs of models, i.e.  AIC(Mi)−AIC(Mj), BIC(Mi)−BIC(Mj), 
APE_SE(Mi)−APE_SE(Mj), APE_AE(Mi)−APE_AE(Mj), and also in tables 
presenting the choices of forecasting model for all pairs of models. These dif-
ferences in selection criteria are interpreted as follows: the positive differences 
favor the second model over the first one in a pair of models (this means either 
a lower value of information criterion or smaller prediction error for the second 
model), and the negative differences indicate that the first model outperforms 
the second one. The sign of differences in criteria may change in time which 
indicates that one model has become outdated. However, from the forecasting 
point of view the most important is the sign of differences in criteria at the end 
of studied period, therefore the choice of the best forecasting model has been 
made basing on the performance of differences in criteria at the end of sample 
(at least three observations with the same sign of difference in a given  
criterion). 

 Figure 1 (row 1) demonstrates that independently of initial sample size the 
performance of differences in AIC criterion for pairs of models is similar, i.e. 
the AIC criterion favors the AR model over the ARIMA and RW models, and 
the ARIMA model is better in sense of AIC criterion than the RW model. How-
ever, the results for different rolling window sizes are different (Fig. 1, row 2). 
While the dominance of the AR model over ARIMA model is maintained, the 
AIC criterion prefers the RW model over AR and ARIMA model (differences 
in AIC for pairs of models, AIC(ARIMA)−AIC(RW) and AIC(AR)−AIC(RW), 
are positive) what is opposite to results obtained for increasing by one sample 
size (Fig. 1, row 1). The different results for window size of 80 observations in 
comparison with those obtained for window size of 40 and 60 observations 
could suggest the influence of window size on a choice of model by the AIC 
criterion, but in that case it is rather the problem of too large window size with 
regard to the number of observations.  

 The results of model selection for consumer price index (CPI) by the BIC 
criterion seem to be more stable and insensitive as well to the initial sample size 
(Fig. 2, row 1) as rolling window size (Fig. 2, row 2) in comparison with the 
selection by the AIC criterion. The BIC criterion favors the RW model over the 
AR and ARIMA models. As previously the AR is preferred over the ARIMA 
model.    

 Summing up, the choices by information criterion differ, i.e. the AIC crite-
rion prefers the AR model for CPI in the case of increasing sample size (version 



Information and Prediction Criteria in Selecting the Forecasting Model  27

I), and model RW − in the case of rolling window size, version II (except the 
window size of 80 observations), while the BIC criterion prefers the RW model 
in both version. 

 Figures 3 and 4 demonstrate the differences in prediction criteria APE_SE 
and APE_AE respectively. The APE_SE criterion favors the RW model over 
the AR and ARIMA model (Fig. 3, row 1 and 2) except the initial sample size  
and rolling window size of 80 observations when the ARIMA model is pre-
ferred over the RW and AR models. The lack of support for the RW model in 
sample of 80 observations shows rather the influence of initial sample size and 
rolling window size on selecting the model. Hence, the size of initial sample or 
rolling window should not be to large with regard to total number of  
observations.   

 Observing the differences in APE_AE the influence of the size of initial 
sample and rolling window is much more distinct (Fig. 4, row 1 and 2).  
For initial sample size and window size of 40 observations the APE_AE criteri-
on prefers the RW model over the ARIMA and AR models. However, for sam-
ple (or window) of 60 observations this criterion favors the ARIMA model over 
the AR and RW models, and for sample (or window) of 80 observations – the 
AR model over the ARIMA and RW models.  

Table 1. Results of model selection for CPI in Poland using information (AIC, BIC) and 
prediction criteria  (APE_SE, APE_AE) 

Pairs of models 
 

Selection 
criteria 

Version I Version II 

n=40 n=60 n=80 n=40 n=60 n=80 

ARIMA vs. AR AIC AR AR AR AR AR AR 

BIC AR AR AR AR AR AR 

APE_SE ARIMA ARIMA ARIMA AR ARIMA ARIMA 

APE_AE AR ARIMA AR AR ARIMA AR 

ARIMA vs. RW AIC ARIMA ARIMA ARIMA RW RW ARIMA 

BIC RW RW RW RW RW RW 

APE_SE RW RW ARIMA RW RW ARIMA 

APE_AE RW ARIMA ARIMA RW ARIMA ARIMA 

AR vs. RW AIC AR AR AR RW RW AR 

BIC RW RW RW RW RW RW 

APE_SE RW RW AR RW RW AR 

APE_AE RW AR AR RW AR AR 
   



Mariola Piłatowska 28

Table 2. Accuracy measures for one-step-ahead forecasts of CPI from different models 
in the period 2011:01−20011:06 − version I 

Accuracy measures 
 

Models 

ARIMA AR RW 

MSE 0.34 0.35 0.26 

RMSE 0.58 0.59 0.51 

U 1.31 1.36 1.00 

MAPE (%) 0.48 0.46 0.41 

Table 3. Accuracy measures for one-step-ahead forecasts of CPI from different models 
in the period 2011:01−2011:06 − version II 

Accuracy 
measures 

n=40  n=60 n=80 

ARIMA AR RW ARIMA AR RW ARIMA AR RW 

MSE 0.314 0.292 0.265 0.305 0.365 0.276 0.297 0.342 0.279 

RMSE 0.560 0.540 0.515 0.552 0.604 0.526 0.545 0.585 0.528 

U 1.183 1.099 1.000 1.104 1.322 1.000 1.063 1.224 1.000 

MAPE 0.443% 0.434% 0.423% 0.453% 0.470% 0.421% 0.444% 0.450% 0.432% 

 Generally, the RW model should be chosen as the best model for CPI be-
cause it is preferred by all criteria in the case of rolling windows (except win-
dow of 80 observations for APE_SE and APE_AE and window of 60 observa-
tions for APE_AE which seem rather too large with regard to number of obser-
vations) and also in the case of increasing sample size except the AIC criterion 
which favored the AR model and prediction criteria for initial sample size of 80 
observations (for both criteria APE) and of 60 observations (for APE_AE) − see 
Figure 1−4 and Table 1. 

 If the RW model is really the best one, its predictive performance should be 
also confirmed in out-of-sample evaluation. Out-of-sample forecast evaluation 
(i.e. in the period 2011:01−2011:06) has been realized by the measures of accu-
racy (MSE, RMSE, U, MAPE) − see Table 2 and 3.  

 The results in Table 2 and 3 indicate that one-step-ahead forecasts of CPI  
made from the RW model have the smallest prediction errors independently of 
the versions (iteratively increasing sample size by one − version I, or rolling 
window of given size − version II). The out-of-sample performance of RW 
model is in rough agreement with choices received by APE criteria but also BIC 
criterion, thus providing evidence of correct model selection by these criteria. 

 The results of selecting the best model for industry production (IP) in Po-
land are presented in Figures 5−8. Figure 5 shows that the AIC criterion favors 
the AR model over the ARIMA and RW models independently of initial sample 
size and rolling windows. Hence, in that case the selection of a model by the 
AIC criterion seems to be insensitive to the size of initial sample and rolling 



Information and Prediction Criteria in Selecting the Forecasting Model  29

windows. When the BIC criterion has been used the results were similar but 
only in version I (initial sample size increased by one) − see Figure 6, row 1 and 
for window size of 80 observations (version II, see Figure 6, row 2).  
For window sizes of 40 and 60 observations the BIC criterion prefers the RW 
model over the ARIMA and AR model (Figure 6, row 2).     

 The choice of model of industry production (IP) in Poland by prediction 
criteria is different than by information criteria. Namely, the APE_SE criterion 
favors the ARIMA model over the AR and RW model except the initial sample 
of 80 observations (version I) and window size of 80 observations (version II)  
− Figure 7. This dominance of model ARIMA is maintained when the APE_AE 
criterion is used to select the best model (except the initial sample size of 60 
observations, version I) − Figure 8.  

 Summing up, according to information criteria (AIC, BIC) the AR model 
should be chosen as the best model for industry production, IP, (except the 
choice of BIC criterion for rolling window of 40 and 60 observations when the 
RW model is preferred) − see Figure 5−6 and Table 4. Whereas the choice of 
prediction criteria (APE_SE, APE_AE) is the ARIMA model (except initial 
sample of 60 observations) − see Figure 7-8 and Table 4. 

Table 4. Results of model selection for IP in Poland using information (AIC, BIC) and 
prediction criteria  (APE_SE, APE_AE) 

Pairs of models 
 

Selection 
criteria 

Version I Version II 

n=40 n=60 n=80 n=40 n=60 n=80 

ARIMA vs. AR AIC AR AR AR AR AR AR 

BIC AR AR AR AR AR AR 

APE_SE ARIMA ARIMA AR ARIMA ARIMA AR 

APE_AE ARIMA AR ARIMA ARIMA ARIMA AR 

ARIMA vs. RW AIC ARIMA ARIMA ARIMA ARIMA ARIMA ARIMA 

BIC ARIMA ARIMA ARIMA RW RW ARIMA 

APE_SE ARIMA ARIMA ARIMA ARIMA ARIMA ARIMA 

APE_AE ARIMA ARIMA ARIMA ARIMA ARIMA ARIMA 

AR vs. RW AIC AR AR AR AR AR AR 

BIC AR AR AR RW RW AR 

APE_SE AR AR AR RW AR AR 

APE_AE AR AR AR AR AR AR 

 Out-of-sample evaluation of IP forecasts (i.e. in the period 
2011:01−2011:06) has been realized by the measures of accuracy (MSE, 
RMSE, U, MAPE) − see Table 5 and 6.  

 The results in Table 5 and 6 show that both the ARIMA model and AR 
model have similar predictive value because the accuracy measures of one-step-



Mariola Piłatowska 30

ahead forecasts of IP do not differ much, so these model may complete with 
each other. In case of version I (iteratively increasing sample size by one) the 
RMSE and U measure prefer the ARIMA model as a model with the smallest 
prediction error but the MAPE indicates the AR model (Table 5). The opposite 
result is obtained in version II for rolling window of 40 observations (Table 6).  

Table 5. Accuracy measures for one-step-ahead forecasts of IP from different models in 
the period 2011:01−20011:06 − version I 

Accuracy measures 
 

Models 

ARIMA AR RW 

RMSE 2673.30 2679.50 3390.70 

U 0.622 0.624 1.00 

MAPE (%) 2.12 2.03 3.52 

Table 6. Accuracy measures for one-step-ahead forecasts of IP from different models in 
the period 2011:01−2011:06 − version II 

Accuracy 
measures 

n=40  n=60 n=80 

ARIMA AR RW ARIMA AR RW ARIMA AR RW 

RMSE 2916.6 2908.4 3411.8 2716.42 2863.65 3386.73 2787.6 2697.1 3395.6 

U 0.731 0.727 1.000 0.643 0.715 1.000 0.674 0.631 1.00 

MAPE (%) 2.390 2.460 3.510 2.12% 2.210 3.500 2.220 1.990 3.520 

For the window of 60 and 80 observations the ARIMA model and AR model 
give the smallest prediction errors. It is worth noting that the ARIMA and AR 
models substantially outperform the RW model. On the whole, the predictive 
performance of ARIMA and AR models is in agreement with choices obtained 
by APE criteria and AIC criterion.  

Conclusions 

 The results of choosing the forecasting model on empirical data for Poland 
showed that the size of initial sample (version I) and rolling windows (version 
II) do have an impact on the choice of forecasting model (within a given ver-
sion), especially it concerns the APE. The size of initial sample and rolling win-
dows should be relatively small with regard to sample size because too large 
initial sample (or window) enables to follow the evolution of APE for sufficient 
number of periods. There are no relevant differences between the selection of 
forecasting model for the initial sample and rolling windows (within the com-
parative number of observations). Therefore it seems sufficient to calculate the 
APE only for some small initial sample size increasing iteratively by one obser-
vation. Both prediction and information criteria are useful in selecting the fore-
casting model, however the choice of models by prediction criteria is supposed 
to be much more in agreement with their best out-of-sample performance. 



Information and Prediction Criteria in Selecting the Forecasting Model  31

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Kryteria informacyjne i predykcyjne w wyborze modelu prognostycznego  

Z a r y s  t r e ś c i. Celem artykułu jest porównanie zachowania się kryteriów informacyjnych 
i predykcyjnych w wyborze modelu prognostycznego na podstawie danych empirycznych dla 
Polski, przy założeniu nieznajomości modelu generującego dane. Uwaga będzie poświęcona 
śledzeniu zmian kryteriów informacyjnych (AIC, BIC) oraz skumulowanego błędu prognoz 
(APE) dla próby powiększanej iteracyjnie o jedną obserwację i ruchowych okien (o różnej wiel-
kości), a także ocenie wpływu wielkości próby (startowej) i ruchomego okna na wybór modelu 
prognostycznego. Wybór najlepszego modelu prognostycznego jest dokonywany spośród nastę-
pującego zestawu modeli: model autoregresyjny (AR, z trendem i bez trendu deterministyczne-
go), model ARIMA, model błądzenia przypadkowego (RW).  

S ł o w a  k l u c z o w e: kryteria informacyjne, kryteria predykcyjne, skumulowany błąd predyk-
cji, wybór modelu.  



   

   

Figure 1.  Differences in AIC information criterion (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA vs. 

RW, AR vs. RW) depending on starting sample size and size of rolling window for CPI in Poland 

 

 



   

   

Figure 2.  Differences in BIC information criterion (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA vs. 

RW, AR vs. RW) depending on starting sample size and size of rolling window for CPI in Poland 

 



   

   

Figure 3.  Differences in prediction criterion APE_SE (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA 

vs. RW, AR vs. RW) depending on starting sample size and size of rolling window for CPI in Poland 



   

   

Figure 4.  Differences in prediction criterion APE_AE (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA 

vs. RW, AR vs. RW) depending on starting sample size and size of rolling window for CPI in Poland 

 



   

   

Figure 5.  Differences in AIC criterion (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA vs. RW, AR 

vs. RW) depending on starting sample size and size of rolling window for IP in Poland 

 



   

   

Figure 6.  Differences in BIC criterion (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA vs. RW, AR 

vs. RW) depending on starting sample size and size of rolling window for IP in Poland 

 



   

   

Figure 7.  Differences in prediction criterion APE_SE (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA 
vs. RW, AR vs. RW) depending on starting sample size and size of rolling window for IP in Poland 

 



   

   

Figure 8.  Differences in prediction criterion APE_AE (version I - row 1, version II - row 2) for pairs of models (ARIMA vs. AR, ARIMA 

vs. RW, AR vs. RW) depending on starting sample size and size of rolling window for IP in Poland 

 



 
 


	02_Piłatowska_M
	Piłatowska DEM 2011 wykresy

