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We similarly suppose that there is no autoregressive lag 6. The estimated results are presented as follows in table 1 7 : Table 1. This non linearity is caused by the existence of a cyclical asymmetry. This last concept can be proved through the use of asymmetry tests. This result sustains our assumption that suggests that three state model is more favourable than the two state model 8. Also by considering the AIC criterion, three states Markov switching is the best model.

The estimation of the model MSIH 3 -AR 0 , in which the intercept and the variance shift from one regime to another, supports the existence of a primary low growth regime.

In fact, the intercept or the mean 9 related to the first regime is negative and significant. The most important recession phase that known Tunisia during the period of analysis, is the one that began with the Arab Spring, which is propagated after that to Egypt, Yemen, Libya and Syria. But, due to the Libyan revolution the recession phase in Tunisia does not persist for a long way.

## [PDF] Advances in Markov-Switching Models: Applications in Business Cycle Research and Finance

In effect legal and illegal transactions from Tunisia to Libya remain rapidly the economic activity stable with a moderate growth in Tunisia and the economic activity does not enter in a long recession phase. This moderate growth phase, which corresponds to the second regime, is the most highly period in Tunisia with an average duration of about 12 months and a probability of staying in this phase of about 0. According to the matrix of transition probabilities, as represented in table 2, the high growth phase lasts in average 8.

Following these results, we deduce that the economic activities in Tunisia have witnessed an important period of stability characterised by a positive growth rate. But, due to both external and internal crisis, the economic activity know some but few negative recession period which strongly hit the economic activity. Table 2.

In what follows, we try to determine the business cycle turning points by using the smooth probabilities and certain decision rules. A Turning Point Chronology for the Tunisian Industrial Production A basic question about which policy makers and economic agents are concerned, deals with the detection and the forecast of the switch among the business cycle phases. In this section, we are trying to determine the expansion and recession periods in the Tunisian economic activity. In fact, we notice the absence of any committee interested in this kind of work in Tunisia; even the economic agents along with the political decision makers anticipate the periods of crisis by intuition.

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In this research, we try to use the index series related to industrial production a reference in our bid to determine the cyclical turning points during the same period about which we have estimated our model. The reasons of our choice are twofold: first being the fact that, in most previous works, we have chosen this series as a reference for the economic activity. The second of which being the fact that the validity of this series for a long period at a monthly frequency.

Similarly to what has been applied to the two-state model, we are trying to present in this paper the different dating of the economic-cycle turning points by using the three-state switching regime model as has just been estimated above. The main advantage we can mention in favour of these parametric models as compared to the non parametric methods, for instance the turning points dating method of Bry and Boschan, is its ability to determine the turning points for more than two regimes.

### Forecasting US interest rates and business cycle with a nonlinear regime switching VAR model

These smoothed probabilities are used for the classification of the observations among the three regimes. The classification rule is very simple and consists in assigning each observation in the regime with the highest probability. These rules are the following: i. Peaks and troughs must alternate. A phase must last at least six months. A cycle must have a minimum duration of fifteen months. By considering these properties, after estimating the MSIH 3 -AR 0 model over the period from to , and after determining the smoothed probabilities, we obtain the following turning points.

Figure 2.

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Mean of industrial production growth rates and smoothed, filtered and forecasted probabilities from the MSIH 3 -AR 0 model Following the results obtained in table 3 and the graphics below it, we note that economic activity move from the recession phase or recovery phase to the moderate growth rate and reciprocally. There is no motion from the recession phase to the recovery phase or from the recovery to the recession.

It is clear also that, like in developed countries, normal periods corresponding to moderate positive growth rate are higher than recession and high growth recovery phases. Then, we can conclude that during normal phase Tunisian economic activity is driven persistent chocks, while it is driven by transitory chocks during recession and recovery phases.

Table 3. Due to the persistence of this recession and the economic and social problems that knows this country in this period, the Tunisian people's protests against the government. These events led to the Arab Spring in January But as we said above, this important event didn't too persist due to the propagation of this revolution to Libya. Forecasting After estimating the switching regime models, in order to analyse the economic activity in Tunisia, we are now interesting at the ability of the Markov switching models to forecast the industrial production in Tunisia.

To do this, we consider two different Markov switching models: the two state as well as the three state models Our objective is to determine the best forecasting model of the economic activity in Tunisia. To establish a comparison between two models, we have had recourse to the following out-of-sample forecasting procedure Out-of-sample forecasting We estimate the model for the period ranging from up to , and then, we use a recursive out-of-sample procedure from to To obtain the forecasts we should determine at each period the intercept and the predicted filtered probabilities one step ahead.

It must be noted here that the predicted filtered probabilities, for one step ahead, depend only on the usual filtered probabilities and on the transition probabilities, given the independence hypothesis of the state variable s t following a first order Markov chain. This procedure is repeated in a recursive way until the period to obtain the recursive one step prediction. The following graph presents the results of the forecasts obtained for the two different models. According to figure 3 we can see that both the three state model and the two state model provide a good performance in forecasting the Tunisian industrial production index during the periods of Figure 4 give us an idea about the ability of the predictive probabilities, obtained from the both models, to predict the phase of the economic activity.

From these graphs we can see that the predictive probabilities obtained by the two models are very similar to the estimated filtered probabilities, with a slight advantage to the three state model. In effect, when we compare the predictive probabilities, in order to determine the phase of the economic activity, we have only two different points between the forecasted state and the estimated state for the three state model and three different points for the two state model Figure 3.

## Recent Advances in Estimating Nonlinear Models

Forecasts of the tunisian industrial production index Figure 4. Fitted and 1-step predicted probabilities To evaluate the forecast accuracy of the three state Markov-switching model relative to that of the two state model, we propose to use the squared errors MSE and mean absolute errors MAE.

Also, we propose the test of equal forecast accuracy developed by Diebold-Mariano We compared the forecasts from January to October The following table presents the results.

From table 4 the results showed that MSE are Also, we obtained MAE of about 2. Therefore, we can conclude that the three state Markov switching model achieves superior forecasts relative to the two state Markov switching. This confirms the results already obtained in the first part of this paper, where we have preferred the three regime switching model to the two state model. Also, this result confirms the results obtained in the empirical literature, for which the non linearity of the switching regimes model is able to analyse the economic cycle's variability.

Table 4.

## Research | Personal Website of Candelon Bertrand

Conclusions This study uses Markov switching models for estimating, dating and forecasting the economic activity in Tunisia during the two last decades. In particular, the optimal probabilities interferences determined from the Markov switching models are used to define the different phases of the cyclical economic fluctuations emphasizing the Tunisian real production.

In fact, in this paper we estimate a three regime Markov switching model for monthly industrial production growth rate over the period —, in which the intercept and the variance are allowed to vary given the state of the economy. The specification tests show that the Markov switching model is a powerful technique for analysing the Tunisian business cycle.

And the parametric steepness test of asymmetry suggests that the three regime Markov switching model represents the Tunisian economic activity better than the two regime model. On the other side, we conclude that the non linear three state Markov switching model displays a better out-of-sample forecasting performance than the two state Markov switching model. This conclusion has been confirmed when using a comparison based on the predictive performance of the two and three-state models. In fact, the filtered probabilities from the switching regime models allow us to obtain forecasts very close to the reality and to prefer the three-state model.

Moreover, to recognize in advance the economic transition relating to a new phase of the economic cycle, we can consider the Markov switching models as an adequate tool able to determine the dating evaluation of the economic cycles, so as to present the forecasts concerning the real economic activity fluctuations in Tunisia. Notes 1. Keynes has indicated that the time series "unemployment" is characterised by sudden jumps.

In fact, our ultimate objective is to analyse the cyclical asymmetries. The Markov switching models are known for their empirical success to analyse such asymmetries mainly during the analysis of the American economic series such as the gross national product. In most of the works concerning the business cycle asymmetries, we use the industrial production series as a reference series.

For estimation purposes, as time series concerning the period under our review is not stationary, we consider the month growth rates series in order to exclude the short-term fluctuations.