Determinación de la humedad del cacao en grano

In chapter 4 we identified 4 market regimes for corn. The full length of the data captures weekly observations from January 1995 until April 2014. Regime 1 is the period of time between January 13th_{, 1995 and January 11}th_{, 2008 with 669 observations; regime 2 is the period between}

January 11th, 2008 and December 12th, 2008 with 48 observations; regime 3 is the period between December 12th, 2008 and June 21st, 2013 with 236 observations; and regime 4 is the period between June 21st, 2014 and April 25th, 2014 with 44 observations.

Table 5.1, Test for Forecast Bias - Corn

Test Full Period R1 R2 R3 R4

1. IV model Y Y Y Y Y

2. HV model Y Y Y Y Y

3. Composite model Y Y Y Y Y

4. Naïve model Y Y Y Y Y

*Y= The forecast method is unbiased. *N= The forecast method is biased. * From equation 5.1.2.

Using the test for forecast bias we can conclude that in the case of corn, implied volatility, historical volatility, a linear combination of both and a naïve approach, provide an unbiased method for forecasting future 1-week ahead realized volatility over the full period examined. This conclusion also holds across the four individual regimes.

Table 5.2, Test for Forecast Efficiency- Corn

Test Full Period R1 R2 R3 R4

*Beta efficiency 1. IV model Y Y Y Y Y 2. HV model Y Y Y Y Y 3. Composite model Y Y Y Y Y 4. Naïve model Y Y Y Y Y *Rho efficiency 1. IV model Y N Y Y Y 2. HV model Y Y Y Y Y 3. Composite model Y N Y Y Y 4. Naïve model Y Y Y Y Y

*Y= The forecast passes the beta efficiency/rho efficiency test for weak efficiency. *N= The forecast fails the beta efficiency/rho efficiency test for weak efficiency. *From equations 5.1.3.1 and 5.1.3.2.

Using the forecast efficiency test, we consider a forecast efficient if it passes both conditions of weak efficiency: the beta efficiency and the rho efficiency conditions.

The condition for weak efficiency using the beta efficiency test is satisfied across the four forecast methods when we applied the test to the full period of time. This means that implied volatility, historical volatility, a composite method and a naïve approach, efficiently incorporate all the information regarding future 1-week ahead volatility. This conclusion holds when we applied the test to the four market regimes.

The condition for weak efficiency using the rho efficiency test is also satisfied across the four forecast methods when the test is applied to the full period of time. This suggests that there is no time series pattern to the forecast errors. This conclusion holds across all the regimes and across the four forecast methods analyzed with the exception of regime one. In regime one we found that implied volatility and the composite model fail to pass this condition of weak efficiency.

In conclusion, using the full length of the data we find that implied volatility, historical volatility, a composite method and a naïve approach prove to be efficient forecasters of future 1- week realized volatility. This conclusion holds for regimes two, three and four. In regime one we find that the implied volatility and composite approach are not efficient forecasters of future 1- week realized volatility.

The “beta efficiency test” was consistent across regimes and across forecast methods. In the “rho efficiency test” case, the results for regime 1 (with 669 observations) in the implied volatility model and the composite model proved not to prevail in the full period analysis,

meaning that the period of time contained in regimes 2, 3 and 4 (with a total of 328 observations) have stronger effects on the full period results.

Table 5.3, Test for Forecast Encompassing- Corn

Test Full Period R1 R2 R3 R4

Preferred forecast 1. Implied Volatility Y Y Y Y N 2. Historical Volatility N N Y N Y Preferred forecast 1. Implied Volatility Y Y Y Y Y 2. Naïve model N N Y N Y Preferred forecast 1.Historical Volatility Y Y Y Y Y 2. Naïve model N N Y Y N

*Y= The forecast encompasses the information contained in the alternative forecast. *N= The forecast does not encompass the information contained in the alternative forecast. *From equation 5.1.4.

The test for forecast encompassing evaluates if the preferred forecast encompasses all the information provided by the alternative forecast. In our analysis we first set up implied volatility to be the preferred forecast and historical volatility to be the alternative forecast then we flipped the test specification to have historical volatility as the preferred forecast and implied volatility be the alternative forecast. Later, we set up implied volatility to be the preferred forecast and

naïve approach to be the alternative forecast then we flipped the test specification to have the naïve approach as the preferred forecast and implied volatility be the alternative forecast. Lastly, we set up historical volatility to be the preferred forecast and naïve approach to be the alternative forecast then we flipped the test specification to have the naïve approach as the preferred forecast and historical volatility be the alternative forecast.

In the full period scenario, the implied volatility forecast method encompasses all the information contained in the historical volatility forecast method. Implied volatility forecast method encompasses all the information contained in the naive forecast method. Historical volatility forecast method encompasses all the information contained in the naive forecast method. This result is reversed when we changed the preferred methods. As expected, implied volatility does contain useful information beyond historical volatility, meaning historical volatility did not encompass all the information contained in an implied volatility forecast. The naïve approach did not encompass the information contained in an implied or historical volatility approach. The results for each regime can be interpreted similarly.

The full period results might be driven by the results in regimes one and three in the historical volatility forecast method. This suggests that regimes one and three have stronger influence on the results in the full period, where historical volatility was found not to encompass the information contained in the implied volatility forecast method. In the analysis of the implied volatility forecast method, the results from the full period are driving those of the regimes one, two and three.

Table 5.4, Test for Time Change- Corn

Test Full Period R1 R2 R3 R4

1. IV model Y+ Y+ Y+ N N

2. HV model Y+ Y+ N N N

3. Composite model Y+ Y+ N N N

4. Naïve model Y+ Y+ N N N

*Y+= The forecast errors are getting bigger overtime. *Y- _{= The forecast errors are getting smaller overtime.}

*N= The forecast does not show systematic change over time. *From equation 5.1.5.

Using the test for time change for the full period of time we find that the implied

volatility, the historical volatility, a composite approach and naïve approach all show systematic change over time. Specifically, the forecast errors generated by these four forecasts are getting bigger and therefore the forecast has not improved over time. For the market regimes we find different results; for example in regimes 3 and 4, we did not find systematic change in the forecast over time across the forecast methods. For specific information regarding the magnitude of the change please refer to the annex section.

We believe that the results from the regime 1 are driving the conclusions for the results using the full period of time. This might be intuitive given that the length of the regime 1 is considerably bigger compared to the length of the regimes 2, 3 and 4. More specifically we believe that the 3 forecasts methods increased their forecast errors in the first regime (1998- 2008) given that the volume and open interest was lower compared to more recent periods.