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ThesisItem Open Access A COMPARISON OF ALGEBRAIC MODELS TO DESCRIBE THE LACTATION CURVES IN JAFARABADI BUFFALO 3384(JAU JUNAGADH, 2021-09) CHUDASAMA HARSHAL MOHANLAL; Dr. N. J. RankjaThe present investigation aims to compare the efficiency of seven Algebraic models with respect to weekly milk yield records of Jafarabadi buffalo. The weekly milk yield (litre) data were collected for 357 record of six lactations covering the period from 2009 to 2018 of the Cattle Breeding Farm, Junagadh Agriculture University, Junagadh. The weekly milk yield records of 43 weeks for each of the six lactations and average of all the six lactations (overall) were subjected to statistical analysis based on seven different models viz., Inverse polynomial, Gamma type, Parabolic exponential, Exponential, Quadratic, Quadratic cum log and model proposed by Morant and Gnanasakthy using non-linear fitting approach. The two criteria employed to judge the efficiency of different models were coefficient of determination (R2) and deviation from regression sum of squares (DSS). Apart from this, different characteristics viz., initial milk yield (litre/week), peak milk yield (litre), time to attain peak milk yield (week), 43rd week milk yield (litre), rate of increase (litre), rate of decrease (litre) and total milk yield (litre/lactation) were estimated and compared with the observed data in each lactation and overall, i.e. average of six lactations. The Quadratic cum log model was found most efficient based on both the criteria i.e. R2 and DSS. Next in order was Gamma model followed by Parabolic exponential for all the six lactations and overall basis (average of six lactations). Since both the criteria i.e. R2 and DSS were highly negatively correlated either of them can be considered for comparing efficiency of different algebraic models. It was also observed that the variation in coefficient of determination (R2) was less for all the models tried in each of the lactation whereas it was comprehensive in the case of deviation from regression sum of squares (DSS). Various useful characteristics of lactation curve viz., initial milk yield, peak milk yield, time to attain peak milk yield, milk yield in 43re week (last week), rising and declining phases and total milk yield were estimated for four out of seven models, i.e. Gamma type model, Quadratic cum log model, Quadratic model and Inverse polynomial model. These models were compared for various characteristics based on observed records. Inverse polynomial model, model proposed by Morant and Gnanasakthy and Exponential models were excluded from comparison as they did not provide logical estimates for these characteristics. Performance of the models varied with the characteristics of milk yield of different lactations. Gamma type model was found most efficient for time to attain peak milk yield and rate of increase. However, Gamma model showed superiority to predict rate of decrease. To predict initial milk yield as well as peak milk yield, Quadratic cum log model was found superior as compared to rest of the models. Quadratic model less efficiency to estimate various characteristics of milk yield records of Jafarabad buffaloThesisItem Open Access “A STATISTICAL ANALYSIS ON MARKET INTEGRATION AND PRICE FORECASTING OF DOMESTIC AND INTERNATIONAL WHEAT MARKETS”, T3217(JAU JUNAGADH, 2021-01) Sabhaya Ankit G.; Sabhaya Ankit G.Wheat (Triticum spp.) is one such important commodity in India that enjoys at least 40 per cent procurement under minimum support price (MSP) mechanism. Despite that, farmers outside the procurement bracket fail to realize remunerative prices in the open markets. In this connection, marketing plays an important role in the economic development as it stimulates production and avoids unnecessary fluctuation in output. The Market integration analyses were also carried out by using Granger bivariate co-integration test and Johansen multivariate co-integration test. These tests revealed long-run equilibrium between these markets and the causality test indicates the existence of feedback relationship between Rajkot, Junagadh, Mathura (UP), Khanna (Punjab), Argentina and USA markets. As a preliminary, the Augmented Dickey-Fuller test were conducted and it detected the presence of unit root in the price series at levels for all the three markets and the stationary, which indicate price transmission occur between the markets. The Vector Error Correction model (VECM) captured the short-run adjustment towards the long-run equilibrium between the markets and the adequacy of the fitted VECM is also checked. Granger causality test was attempted to determine the direction of price influence in-between the market pairs. The findings revealed bidirectional causality among all the local and national pairs. On the flip side, the international markets were completely devoid of any type of causality with domestic markets. Price transmission occur effectively and there was also a well infrastructure facility to meet the proper good allocation in the studied markets. The volatility and market integration analysis were carried out in selected wheat markets from January, 2003 to December, 2019 by using various statistical models available in the time series literature. Volatility in these markets were analyzed by using the novel univariate autoregressive integrated moving-average (ARIMA) model, conditional heteroscedsatic GARCH model and Vector Auto regression (VAR) model. Price forecasting was attempted using ARIMA, ARCH/ GARCH and VAR models and the results were compared. The following models were found to be fit in case of ARIMA: Rajkot (2,1,2); Junagadh (3,1,2); Mathura (2,1,1); Khanna (1,1,1); USA (2,1,3); and Argentina (2,1,2) on the basis of minimum value of MAPE, AIC, BIC and higher value of adj. R2 . Cross-validation (i.e. out of sample forecasts) for the 12 month period from Jan. 2019 to Dec. 2019 revealed the robustness of the selected models as the forecasting errors in all the cases were found to be <10 per cent. GARCH effect was found valid only in Khanna (Punjab) market and VAR was attempted for all the markets. On the basis of forecasting criteria, ARIMA was found to be best suitable when compared to VAR in all the marketsThesisItem Open Access AN EMPIRICAL COMPARISON OF DIFFERENT METHODS OF SIRE SELECTION: A BREEDING VALUE APPROACH 2916(JAU, JUNAGADH, 2019-08) PATEL VEDANGI ASHOK; D. V. PateA total of 323 daughters of 44 sires maintained for first lactation records and 833 daughters of 44 sires maintained for all lactation records at Cattle Breeding Farm, Junagadh Agricultural University, Junagadh from 1988-2017 were analysed to compare various sire evaluation methods for 300-DMY, LL and CI. Sire evaluation was done using conventional indices (viz. Modified Simple Daughter Average index, Equiparent index, Norton index, Rice index, Tomar index, Corrected Daughter Average index, Contemporary Comparison method and Corrected Contemporary Comparison method), Least Squares method (LS), Best Linear Unbiased Prediction (BLUP) and Average Information Restricted Maximum Likelihood Method (AIREML). BLUP and AIREML models were constructed using univariate models, repeatability models, multivariate models using three traits in all possible combination for first lactation records as well as all lactation records. Criteria for comparison of all the models involved error variance to measure the efficiency of models, additionally, coefficient of determination (%) (R 2 values) and coefficient of variation (CV%) were used to measure the accuracy and stability of models respectively for LS, BLUP and AIREML. The results indicated that the I-1 model and LS models were found to be quite satisfactory looking % relative efficiency (99.25), error variance (2566.31 kg2 ), range (420.13 kg) and % proportion of sires having equal or more breeding values than average for 300-DMY. For LL, AF-23 model was found satisfactory looking to ABSTRACT% relative efficiency (100%), error variance (752.44 days2 ), range (293.24 days) and % proportion of sires having equal or more breeding values than average (52.27%) followed by models AF-123 and I-1 & LS with nearby result with AF-23. For CI, AF 23 model was found satisfactory looking to % relative efficiency (100), error variance (463.76 days2 ), range (251.77 days) and % proportion of sires having equal or more breeding values than average(68.18). The next best models were BF-123 with 98.25% and I-1 & LS with 89.40% relative efficiency. The rank correlation among all conventional indices and Least Square were found positive and highly significant for 300-DMY and CI under study except the rank correlation of I-1 for LL. For 300-DMY, AF-12 was inferred as the most efficient model of sire evaluation with the least variance, while LS and I-1 were found next best models with 2566.31kg2 error variance. LS with relative accuracy 97.87% was observed as next best accurate models after BF-13 (100%). LS model had their lower CV% as compared to other models. LS had highest stability for 300-DMY. The sires having Id 5, 24, 27 and 37 out of top ten sires were commonly selected by the most efficient, accurate & stable models AF-12, BF-13 and LS, respectively. For LL, AF-23 model was found the most efficient model with least within sire variance (752.44 days2 ) while, LS and I-1 had 98.27% relative efficiency. BF-12 was more accurate with 83.2% R2 value and was considered as the most accurate method, followed by LS and I-1. AF-12 had highest stability in LL with lowest CV%. The sires having Id 24, 29 & 35 out of top ten sires were commonly selected by the most efficient, accurate and stable models AF-23, BF-12 and LS, respectively. For CI, AF-23 showed least error variance and thus was inferred as the most efficient method, while, LS had 89.40% relative efficiency. BF-23 had the highest accuracy with R2 (92.45%) among all the models. The next best accurate model was BF-123. Looking to the stability criteria, LS had lower CV% among all models showing. Thus, LS was inferred as most stable model. None of the sires out of top ten were commonly selected by the most efficient, accurate and stable models AF-23, BF-23 and LS, respectively, but sire Id 29 and 36 were selected as common by AF-23 and BF-23 models. It is clear that all first lactation models (F-models) had lower R2 values, had higher CV% and error variance values than their corresponding all lactation models (A-models). Thus use of all lactation records leads to increase in accuracy, stability and efficiency of predicting breeding values for 300-DMY, LL and CI. For 300-DMY AF-12, BF-13 and LS proved to be most efficient, most accurate and most stable model, respectively, while. AF-23, BF-12 and AF-12 proved to be most efficient, most accurate and most stable model, respectively for LL. For CI AF-23, BF-23 and LS proved to be most efficient, most accurate and most stable model, respectively. Use of models incorporating all lactation records instead of those incorporating first lactation records for sire evaluation provided more accuracy, stability and efficiency for all traits. Hence, sire evaluation must be done considering all the available lactation records of the animals.ThesisItem Open Access STATISTICAL EVALUATION OF DIFFERENT METHODS FOR PREHARVEST FORECASTING OF GROUNDNUT YIELD IN JUNAGADH DISTRICT OF GUJARAT 2899(JAU, JUNAGADH, 2019-08) SATHEES KUMAR K; M. S. ShitapA timely and reliable forecast of crop yield needs more emphasis for monsoon dependent country like India where, the economy is mainly based on agricultural production. Weather is a major factor affecting crop production in advanced agricultural systems. The large variation in yield from year to year and place to place is dominated by the weather parameters. In view of fluctuating weather effects, a timely and reliable forecast of crop productivity could help in deciding the policies. A proper forecast of production of commercial crops is very important in an economic system. There is close association between crop productions with prices. An unexpected decrease in production reduces marketable surplus and income of the farmers and leads to prices rise. An efficient forecasting is thus a pre-requisite for food supply information system at district and state level. The present study has been taken up to, (1) To identify the nature of effect of weather variables and time period on groundnut yield in Junagadh district of Gujarat, (2) To explore the possibility of suggesting suitable statistical method for pre-harvest forecasting of the groundnut yield in Junagadh district of Gujarat and (3) To compare the efficiency of MLR and ARIMA models. To estimate the effect of weather variables and time period, yield and weather data for 31 years (1985 to 2015) were used. The weekly averages of weather variables viz., maximum temperature (MAX T), minimum temperature (MIN T), morning ABSTRACTrelative humidity (RH1), afternoon relative humidity (RH2) and weekly total rainfall (RF) from 24th to 37th standard meteorological week of the respective year were considered in the study. In all five approaches were used in the study. Out of these, four approaches used weather variables which were further categorized as based on generated weather variables (correlation coefficient as weight and week number as weight) and based on original weather variables (week wise approach and crop stage wise approach). Three sets of multiple linear regression equations consisting of 23, 24 and 25 years data considering the data up to 10, 12 and 14 weeks for each model were fitted. In addition to this, ARIMA model which used only time series yield data was also used. Similarly, three sets of ARIMA model consisting 23, 24 and 25 years data for each model were fitted. The models based on 10 weeks with 25 years data using correlation coefficient as weight with generated weather variables and model based on 10 weeks with 23 years data using week-wise approach using original weather variables were recommended as pre-harvest forecast models for groundnut productivity of Junagadh district which can predict the groundnut yield 6 weeks before harvest. In case of ARIMA model, ARIMA (1, 1, 1) with 25 years data can be considered as the forecasting model for groundnut productivity in Junagadh district of Gujarat. The comparison between the selected regression models and ARIMA model on the basis of R2 , R̅2 , RMSE and MAE values showed that regression models were superior as compared to ARIMA models. The proposed models are Model based on correlation coefficient as weight using generated weather variables Y= -3536.86 + 1.24Z141 + 5.95Z121 + 15.27Z51 + 1.37Z131 – 41.73Z31 (R̅2 =86.30%) Model based on week-wise approach using original weather variables Y = -6605.93 + 105.81 X45 + 456.09 X25 + 2.94 X38 -27.27 X510 - 456.42 X210 (R̅2=85.70%)ThesisItem Open Access “GROWTH AND INSTABILITY ANALYSIS OF GROUNDNUT CROP IN GUJARAT: BEFORE AND AFTER Bt-COTTON” 2805(JAU, JUNAGADH, 2019-06) PATEL VISHVABEN PRAMODBHAI; M. S. ShitapA major increase in cotton area was observed in Gujarat, replacing by groundnut in the Saurashtra region. As the agricultural production is subjected to extent of variation, the growth and instability in agriculture has remained the subject of deep concern in the area of agricultural economics in India and this is true for oilseeds production also. Instability in agricultural production is also important for agricultural product management. Hence, a critical analysis of growth and instability of groundnut production have its own significant importance. Besides instability, Indian agriculture is also known for sharp variations in agricultural productivity across space which results in various types of disparities. The present study has been taken up, i. To study different statistical models for the growth in area, production and productivity of groundnut crop in Gujarat. ii. To measure the extent of variation in area, production and productivity of groundnut crop in Gujarat. iii. To examine the inter district inter region variability in area, production and productivity of groundnut crop in Gujarat The time series data on area, production and productivity of groundnut crop for 31 years were collected for major groundnut growing districts and Gujarat state ABSTRACT for the period 1985-86 to 2015-16 from Directorate of Agriculture, Gandhinagar, Gujarat State. The entire study period was divided into two sub-periods on the basis of introduction of Bt- cotton as pre Bt-cotton and post Bt- cotton. Various polynomial as well as ARIMA model was used to study the growth. Instability in the area, production and productivity of groundnut was analyzed using the Cuddy Della Valle Index (CDVI) and Friedman test was used to study the inter district and inter regional variability. The results revealed that the area under groundnut was decreased in Bhavnagar, Jamnagar, Junagadh, Kheda, Rajkot and Sabarkantha districts after introduction of Bt-cotton. The production of groundnut was increased in Ahmedabad, Banaskantha, Rajkot and Sabarkantha districts whereas decreased in Jamnagar district and remained stable in Surat district after introduction of Bt-cotton. Productivity was increased in Banaskantha, Bhavnagar, Jamnagar, Junagadh, Rajkot, Sabarkantha and Surendranagar districts after introduction of Bt-cotton. Majority of the districts showed medium level of variability for area except Ahmedabad, Banaskantha, Kheda and Surat (High variability), Rajkot (Low variability), all the districts showed high level of variability for production and high level of variability for productivity except Kheda, Surat and Surendranagar which showed medium level of variability. Significant variability was observed among districts and regions with respect to area under groundnut, production and productivity of groundnut.ThesisItem Open Access AN EMPIRICAL COMPARISON OF DIFFERENT METHODS OF SIRE SELECTION: A BREEDING VALUE APPROACH 2916(JAU, JUNAGADH, 2019-08) Patel Vedangi A.; Dr. D. V. PatelA total of 323 daughters of 44 sires maintained for first lactation records and 833 daughters of 44 sires maintained for all lactation records at Cattle Breeding Farm, Junagadh Agricultural University, Junagadh from 1988-2017 were analysed to compare various sire evaluation methods for 300-DMY, LL and CI. Sire evaluation was done using conventional indices (viz. Modified Simple Daughter Average index, Equiparent index, Norton index, Rice index, Tomar index, Corrected Daughter Average index, Contemporary Comparison method and Corrected Contemporary Comparison method), Least Squares method (LS), Best Linear Unbiased Prediction (BLUP) and Average Information Restricted Maximum Likelihood Method (AIREML). BLUP and AIREML models were constructed using univariate models, repeatability models, multivariate models using three traits in all possible combination for first lactation records as well as all lactation records. Criteria for comparison of all the models involved error variance to measure the efficiency of models, additionally, coefficient of determination (%) (R 2 values) and coefficient of variation (CV%) were used to measure the accuracy and stability of models respectively for LS, BLUP and AIREML. The results indicated that the I-1 model and LS models were found to be quite satisfactory looking % relative efficiency (99.25), error variance (2566.31 kg2 ), range (420.13 kg) and % proportion of sires having equal or more breeding values than average for 300-DMY. For LL, AF-23 model was found satisfactory looking to ABSTRACT% relative efficiency (100%), error variance (752.44 days2 ), range (293.24 days) and % proportion of sires having equal or more breeding values than average (52.27%) followed by models AF-123 and I-1 & LS with nearby result with AF-23. For CI, AF 23 model was found satisfactory looking to % relative efficiency (100), error variance (463.76 days2 ), range (251.77 days) and % proportion of sires having equal or more breeding values than average(68.18). The next best models were BF-123 with 98.25% and I-1 & LS with 89.40% relative efficiency. The rank correlation among all conventional indices and Least Square were found positive and highly significant for 300-DMY and CI under study except the rank correlation of I-1 for LL. For 300-DMY, AF-12 was inferred as the most efficient model of sire evaluation with the least variance, while LS and I-1 were found next best models with 2566.31kg2 error variance. LS with relative accuracy 97.87% was observed as next best accurate models after BF-13 (100%). LS model had their lower CV% as compared to other models. LS had highest stability for 300-DMY. The sires having Id 5, 24, 27 and 37 out of top ten sires were commonly selected by the most efficient, accurate & stable models AF-12, BF-13 and LS, respectively. For LL, AF-23 model was found the most efficient model with least within sire variance (752.44 days2 ) while, LS and I-1 had 98.27% relative efficiency. BF-12 was more accurate with 83.2% R2 value and was considered as the most accurate method, followed by LS and I-1. AF-12 had highest stability in LL with lowest CV%. The sires having Id 24, 29 & 35 out of top ten sires were commonly selected by the most efficient, accurate and stable models AF-23, BF-12 and LS, respectively. For CI, AF-23 showed least error variance and thus was inferred as the most efficient method, while, LS had 89.40% relative efficiency. BF-23 had the highest accuracy with R2 (92.45%) among all the models. The next best accurate model was BF-123. Looking to the stability criteria, LS had lower CV% among all models showing. Thus, LS was inferred as most stable model. None of the sires out of top ten were commonly selected by the most efficient, accurate and stable models AF-23, BF-23 and LS, respectively, but sire Id 29 and 36 were selected as common by AF-23 and BF-23 models. It is clear that all first lactation models (F-models) had lower R2 values, had higher CV% and error variance values than their corresponding all lactation models (A-models). Thus use of all lactation records leads to increase in accuracy, stability and efficiency of predicting breeding values for 300-DMY, LL and CI. For 300-DMY AF-12, BF-13 and LS proved to be most efficient, most accurate and most stable model, respectively, while. AF-23, BF-12 and AF-12 proved to be most efficient, most accurate and most stable model, respectively for LL. For CI AF-23, BF-23 and LS proved to be most efficient, most accurate and most stable model, respectively. Use of models incorporating all lactation records instead of those incorporating first lactation records for sire evaluation provided more accuracy, stability and efficiency for all traits. Hence, sire evaluation must be done considering all the available lactation records of the animalThesisItem Open Access An empirical study on comparison of different methods of stability analysis in groundnut {Arachis hypogea (L.))(JAU,JUNAGADH, 2011-07) PATEL DHANESHKUMAR VELJIBHAI; Dr. H.R.PandyaThesisItem Open Access “AN EMPIRICAL ASSESSMENT OF GENETIC DIVERGENCE IN COTTON (Gossypium hirsutum L.): A MULTIVARIATE APPROACH”(JAU,JUNAGADH, 2018-07) Ramani Bhumika B.; Dr. D. V. PatelThe present investigation was carried out on secondary data of the “Preliminary evaluation trial under irrigated conditions” conducted during kharif – 2015 at Cotton Instructional Farm, Junagadh Agricultural University, Junagadh with 58 genotypes of cotton (Gossypium hirsutum L.). The data were subjected to different statistical analyses viz.; ANOVA, D2 statistical analysis and principal components analysis to assess the magnitude of genetic variability present in the test material, the extent of genetic diversity in cotton, group the genotypes by using Tocher method and identify indicator of genetic diversity of genotypes. The analysis of variance revealed that mean squares due to genotypes were found significant for the days to 50% flowering (139.384**), plant height (161.175**), number of sympodia per plant (4.560**), number of bolls per plant (138.983**), seed cotton yield (kg/ha) (568611.54**), ginning % (8.588**), number of monopodia per plant (1.637*) and seed index (1.480*) except for the boll weight (0.204NS) and lint index (0.549NS). The values of PCV for all the characters were found more than it’s GCV. High estimates of GCV were reported for the characters viz.; number of monopodia per plant (29.99) and seed cotton yield (kg/ha) (21.56), while the number of boll per plant (19.54) had moderate and the remaining characters had low GCV. The characters viz.; number of sympodia per plant (14.0) and plant height (24.0), then the boll weight (44.9), seed index (52.6) and lint index (53.8) and then the ginning percentage (70.3), numbers of bolls per plant (77.8), seed cotton yield (kg/ha) (78.3), numbers of monopodia per plant (94.6) and days to 50% flowering (95.6) were categorized as the characters with low, moderate and high heritability, respectively. The results of test of significance for total D2 values carried out by χ2 test revealed that out of total possible combinations 1653 among 58 genotypes based on 10 characters 47, 40 and 1566 cases were found non - significant, significant and highly significant, respectively. By using Tocher method, 58 genotypes of cotton were grouped into 20 clusters based on genetic divergence assessed by Mahalanobis’ D2 - statistics. Among which, the clusters III, V, VI, XI, XIII, XV, XVI, XVIII and XIX were solitary, the cluster II had 12, the cluster I had 9, cluster ABSTRACT VIII had 8, the cluster IX, X, XII and XIV had 3 and the clusters IV, VII, XVII and XX had 2 genotypes. The maximum intra cluster distance was recorded for the cluster XX (38.04) followed by the cluster XVII (37.36), cluster XIV (34.64), clusters X and I (32.72), cluster VIII (28.42), cluster VII (27.97), IX (26.02), cluster (30.23), cluster XX (38.04), cluster XVII (37.36), cluster XIX (35.89), clusters II (25.57) and IV (21.85). Whereas the inter-cluster distance was maximum between cluster IX and XVI (482.20) followed by cluster XII and XVIII (407.46), clusters IX and XX (393.83), clusters XVIII and XX (393.55), clusters XIX and XX (391.60) and clusters III and XVI (382.10). This suggested that there is wide genetic diversity among genotypes for studied characters. It could be inferred based on the results of percent contributions of different characters towards the total genetic divergence in 58 genotypes of cotton that the days to 50 % flowering contributed maximum (39.75 %) followed by number of bolls per plant (23.23 %), ginning percentage (6.47 %), number of monopodia per plant (6.41 %) and number of sympodia per plant (4.90 %) as they have ranked first 657, 384, 107, 106 and 81 times in all possible pairs of 58 genotypes, respectively so these characters are to be considered as crucial for further breeding programme to improve cotton crop. The result of principal component analysis presented in scree plot revealed that all ten principal components showed greater than one eigen values which contributed 100.00 per cent of total variation among 58 cotton genotypes. By examining scree plot it was evident that first five PCs had been captured considerable variability, among which PC1 and PC2 showed (28.55 %) and (19.18 %) variability with the eigen values (2.86) and (1.92), respectively. The biplot based on factor loadings of 58 genotypes and 10 characters of cotton showed that the lint index, ginning percent, numbers of monopodia per plant, days to 50% flowering, numbers of sympodia per plant and plant height were found crucial among these first two characters had positive and remaining with negative effects to PC1 and PC2, respectively. While 11, 15, 21, 32, 33, 37, 39, 40, 41, 45, 53 and 55 with positive effects and 7, 8, 9, 10, 14, 17, 19, 20, 22, 23, 24, 25, 30 and 58 with negative effects towards the total variation exhibited by PC1 and PC2, respectively were found important. The comparison of results obtained by principal component analysis and D2 statistics analysis showed that except the characters i.e. numbers of bolls per plant the remaining characters viz., days to 50% flowering, ginning %, numbers of monopodia per plant and numbers of sympodia per plant were found crucial. Incase of genotypes viz., G7, G8, G10, G17, G22, G37, G53 and G56 were found to be important, except the genotype viz., G1, G27, G43 and G44ThesisItem Open Access “TREND ANALYSIS OF WHEAT AREA, PRODUCTION AND PRODUCTIVITY IN GUJARAT BY USING STATISTICAL MODELING TECHNIQUES”(JAU,JUNAGADH, 2018-06) A. M. Lakhlani; Dr. N. J. RankjaKey Words: Shapiro and Wilk test, Run test, polynomial model, ARIMA, Autocorrelation Function and Partial Autocorrelation Function.The present investigation was carried out on the polynomial (linear, quadratic and cubic) models were fitted on original data as well as three, four and five year moving averages data. The Autoregressive Moving Average (ARIMA) models were fitted to original time series data after checking the stationary condition, to arrive at a methodology that can precisely explain the fluctuation in area, production and productivity for wheat crop in different districts is Junagadh, Rajkot, Ahmedabad, Sabarkantha, Banaskantha and Kheda districts selected from Gujarat state. Gujarat state to compare different models for the period 1960-61 to 2011-12 (52 years). The error percentage for the selected model was also carried out to test the prediction power. The data from year 1960-61 to 2006-07 were used for model fitting and remaining years for testing the forecast. In polynomial models, the most suitable model was selected on the basis of adjusted R2, significant regression coefficient, root mean square error, mean absolute error, normality (Shapiro and Wilk test) and randomness of residual’s (Run test) distribution. The different ARIMA models (p, d, q) were judged on the basis of autocorrelation function (ACF) and partial autocorrelation function (PACF) at various lags. Among different fitted ARIMA models, the final models were selected on the basis of significant autoregressive and moving average term, Akaike’s Information Criterion (AIC), Schwartz-Bayesian Criterion (SBC) and normality (Shapiro-Wilk test) and randomness of residual’s (Run test) distribution. Suitable model for wheat area was in Junagadh district was ARIMA (0, 1, 1) model reveal that the MAPE was found to be considered low (14.19) in the year 2010 the model forecast value was very much close to the actual value, the error was found to be only 38.02. In compare to area, production and productivity of Junagadh district, the adjusted R2 were 77%, 78% and 64% respectively. ARIMA (0, 1, 1) model is found to be better model to forecast. In the Rajkot district area and production adjusted R2 is 42% and 56% respectively, MAE and MAPE is high (417.74 and 45.9), ABSTRACT (1539.97 and 42.26) but in productivity adjusted R2 78% the ARIMA (0, 1, 1) was found adequate because the MAE and MAPE is low (241.49 and 6.62). The evaluation of fitted ARIMA model for area, production and productivity in Ahmedabad district it is ascertained that in all the series none of the model was found to be adequate the MAPE was not low. They were in the range between ‘25 to 40’. ARIMA (0, 1, 1) area and production the model is underestimated and productivity the model over estimated. The adjusted R2 was 10%, 79% and 76% respectively for Ahmedabad district. Fitted model in the Sabarkantha district area, production and productivity adjusted R2 77%, 20% and 73% respectively, while it reveals that in productivity MAPE was found to be low (10.26) and standard error was also low so this model were forecast future values accurately. Thus ARIMA (1, 1, 1) and ARIMA (0, 1, 3) were ascertained as the better model for area and productivity of Sabarkantha district. In the Banaskantha district for area, production and productivity adjusted R2 was 57%, 71% and 75% respectively the evaluation of fitted ARIMA (2, 1, 0) model for area that found MAE and MAPE was considerably low (135.03 and 18.95). So this model can be employed for the forecast. In production the ARIMA (0, 1, 1) was found very high that MAE and MAPE (595.43 and 30.32). So this model cannot be employed for forecast purpose and productivity is MAE and MAPE (248.66 and 10.32) this one of the model selection criteria. Thus this model can be employed for forecast. In the Kheda district area, production and productivity adjusted R2 was 41%, 76%, and 75 respectively, while their area and production is very high in MAPE (30.91 and 24.42) was found this model is cannot be used to forecast the future values and productivity of Kheda district ARIMA (0, 1, 1) model was found to be appropriate for forecasting purpose due to its low MAPE (14.81). The adjusted R2 value for Gujarat state area, production and productivity adjusted R2 was is 69%, 77%, and 86% respectively, while there is similarly model of the ARIMA (0, 1, 1) model was found in the area and productivity was found to be better model for forecasting as the MAPE given in the (19.39 and 9.58) as compare to production there is high MAPE (26.93) and this could be not be a better model due to its high standard error and MAPE. Thus, in general, because of crucial requirement of model selection criteria in polynomial as well as ARIMA models, few models could get selected. There is need to examine different techniques for fitted the area, production and productivity of wheat.
