Despliege Análisis Predictivo
Diego Campos Patiño
30/7/2020
1: Introducción
La información disponible es: Base lecherías: 4.158 registros Base Comunas: 349 registros. Base quincenas(principal): 371.852 registros. Entrega variable producción(Kilos Leche) y externas(Urea, KgProt, Kgmg,Rcs, entre otras). Pronóstico con horizonte a 6 meses y 5 años.
La base consta de 246 registros, ya segmentados según objetivo. Serie agregada por mes y año. Variable respuesta: Produccion Kilos.
Se transformará a serie para aplicar herramientas de predicción. 1.- Estadísticas Descriptivas. 2.- Análisis de la serie. 3.- Descomposición de la serie. 4.- Ajustes de modelos clasicos (Tiempo, Cuadratica, Logaritmica). 5.- Análisis de tendencia y estacionariedad. 6.- Modelos SARIMA o Arima Integrado. 7.- Selección de modelos 8.- Validación de modelos. 9.- Comparación entre modelos.
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## [1] 246 10## [1] "llave" "mes" "año" "Suma_KILOSLECHE"
## [5] "media_GRASA" "media_PROTEINA" "media_RCS" "media_KGMG"
## [9] "media_KGPROT" "media_UREA"| llave | mes | año | Suma_KILOSLECHE | media_GRASA | media_PROTEINA | media_RCS | media_KGMG | media_KGPROT | media_UREA |
|---|---|---|---|---|---|---|---|---|---|
| 20001 | 1 | 2000 | 20245052 | 3.178212 | 3.127264 | 432.9200 | 286.8114 | 250.6642 | NA |
| 20002 | 2 | 2000 | 16029405 | 3.409251 | 3.155854 | 477.0588 | 238.2175 | 201.7098 | NA |
| 20003 | 3 | 2000 | 18143081 | 3.531100 | 3.323293 | 443.7678 | 280.7360 | 241.8668 | NA |
| 20004 | 4 | 2000 | 17397830 | 3.571439 | 3.374508 | 458.5125 | 265.6883 | 232.4377 | NA |
| 20005 | 5 | 2000 | 17214109 | 3.826723 | 3.409630 | 490.6395 | 278.7805 | 234.6323 | NA |
| 20006 | 6 | 2000 | 15357363 | 3.883996 | 3.409363 | 552.6963 | 258.1912 | 215.3959 | NA |
| 20007 | 7 | 2000 | 15394975 | 3.851616 | 3.298371 | 570.8281 | 266.9118 | 219.4741 | NA |
| 20008 | 8 | 2000 | 16351537 | 3.559430 | 3.160922 | 545.4745 | 280.0647 | 231.8310 | NA |
| 20009 | 9 | 2000 | 18480841 | 3.325882 | 3.155527 | 513.6636 | 314.4971 | 263.4790 | NA |
| 200010 | 10 | 2000 | 24347562 | 3.077707 | 3.270157 | 462.3720 | 378.2846 | 347.4466 | NA |
| 200011 | 11 | 2000 | 26549262 | 3.047855 | 3.287485 | 412.3590 | 400.1748 | 371.0210 | NA |
| 200012 | 12 | 2000 | 26625862 | 3.147532 | 3.176890 | 458.0547 | 402.7566 | 359.3114 | NA |
| 20011 | 1 | 2001 | 23749375 | 3.262135 | 3.150360 | 479.8234 | 389.5148 | 343.0869 | NA |
| 20012 | 2 | 2001 | 19835413 | 3.365938 | 3.251127 | 420.6889 | 339.6162 | 300.2436 | NA |
| 20013 | 3 | 2001 | 21431655 | 3.580635 | 3.391088 | 410.8162 | 395.3470 | 347.5356 | NA |
| 20014 | 4 | 2001 | 20590163 | 3.705926 | 3.355461 | 418.7464 | 383.5839 | 326.1964 | NA |
| 20015 | 5 | 2001 | 19619234 | 3.893726 | 3.356777 | 474.5875 | 378.1028 | 310.5156 | NA |
| 20016 | 6 | 2001 | 17653944 | 4.013913 | 3.365928 | 529.3903 | 353.0496 | 287.8837 | NA |
| 20017 | 7 | 2001 | 17887091 | 3.816634 | 3.213812 | 549.2344 | 362.6025 | 293.1603 | NA |
| 20018 | 8 | 2001 | 19128329 | 3.561738 | 3.135919 | 543.9470 | 377.4764 | 312.9266 | NA |
| 20019 | 9 | 2001 | 22182074 | 3.317547 | 3.131997 | 515.9269 | 419.0466 | 357.1701 | NA |
| 200110 | 10 | 2001 | 28265012 | 3.082759 | 3.180960 | 448.4923 | 488.1399 | 445.5022 | NA |
| 200111 | 11 | 2001 | 29851910 | 3.079663 | 3.202653 | 369.6252 | 510.0835 | 466.4128 | NA |
| 200112 | 12 | 2001 | 30319511 | 3.077776 | 3.088767 | 345.6830 | 515.9168 | 462.6696 | NA |
| llave | mes | año | Suma_KILOSLECHE | media_GRASA | media_PROTEINA | media_RCS | media_KGMG | media_KGPROT | media_UREA | |
|---|---|---|---|---|---|---|---|---|---|---|
| Min. : 20001 | Min. : 1.000 | Min. :2000 | Min. :15357363 | Min. :3.048 | Min. :2.948 | Min. :212.8 | Min. : 238.2 | Min. : 201.7 | Min. :214.2 | |
| 1st Qu.: 20068 | 1st Qu.: 3.000 | 1st Qu.:2005 | 1st Qu.:27022210 | 1st Qu.:3.408 | 1st Qu.:3.281 | 1st Qu.:276.0 | 1st Qu.: 574.3 | 1st Qu.: 513.9 | 1st Qu.:278.9 | |
| Median : 20137 | Median : 6.000 | Median :2010 | Median :36575623 | Median :3.668 | Median :3.362 | Median :319.8 | Median : 992.4 | Median : 905.8 | Median :296.2 | |
| Mean : 64215 | Mean : 6.427 | Mean :2010 | Mean :36861384 | Mean :3.654 | Mean :3.349 | Mean :342.4 | Mean :1010.3 | Mean : 905.1 | Mean :300.8 | |
| 3rd Qu.: 20205 | 3rd Qu.: 9.000 | 3rd Qu.:2015 | 3rd Qu.:44804974 | 3rd Qu.:3.872 | 3rd Qu.:3.427 | 3rd Qu.:400.5 | 3rd Qu.:1379.4 | 3rd Qu.:1249.0 | 3rd Qu.:324.8 | |
| Max. :201912 | Max. :12.000 | Max. :2020 | Max. :68061032 | Max. :4.322 | Max. :3.607 | Max. :579.4 | Max. :2101.4 | Max. :1943.0 | Max. :423.6 | |
| NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :158 |
## Suma_KILOSLECHE media_GRASA media_PROTEINA media_RCS
## Suma_KILOSLECHE 1.0000000 -0.6630257 0.06361620 -0.72057924
## media_GRASA -0.6630257 1.0000000 0.53978824 0.75988948
## media_PROTEINA 0.0636162 0.5397882 1.00000000 0.11757548
## media_RCS -0.7205792 0.7598895 0.11757548 1.00000000
## media_KGMG 0.8147580 -0.1687875 0.42083602 -0.33789279
## media_KGPROT 0.9336910 -0.4157727 0.28847511 -0.53494173
## media_UREA -0.0749687 -0.1018025 0.06493708 0.05079846
## media_KGMG media_KGPROT media_UREA
## Suma_KILOSLECHE 0.8147580 0.9336910 -0.07496870
## media_GRASA -0.1687875 -0.4157727 -0.10180248
## media_PROTEINA 0.4208360 0.2884751 0.06493708
## media_RCS -0.3378928 -0.5349417 0.05079846
## media_KGMG 1.0000000 0.9634626 -0.15857097
## media_KGPROT 0.9634626 1.0000000 -0.10794483
## media_UREA -0.1585710 -0.1079448 1.00000000##
## Pearson's product-moment correlation
##
## data: urea$media_UREA and urea$Suma_KILOSLECHE
## t = -0.63793, df = 72, p-value = 0.5255
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2983565 0.1562059
## sample estimates:
## cor
## -0.07496871.2: Correlación variable UREA vs Kilos
1.3: Impacto de variable UREA en Kilos Producción
##
## Call:
## lm(formula = urea$Suma_KILOSLECHE ~ urea$media_UREA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13430344 -7335977 -2642842 9863382 19613347
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54087343 9310888 5.809 1.58e-07 ***
## urea$media_UREA -19171 30053 -0.638 0.526
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9559000 on 72 degrees of freedom
## Multiple R-squared: 0.00562, Adjusted R-squared: -0.008191
## F-statistic: 0.4069 on 1 and 72 DF, p-value: 0.5255R-cuadrado: -0.008. El p-valor para cada término comprueba la hipótesis nula de que el coeficiente es igual a cero (no tiene efecto). Un p-valor bajo (< 0.05) indica que se rechaza la hipótesis nula. El p-valor para este caso es (0.5255)lo que indica que es estadísticamente No significativo.
2: Analizando los datos como series de tiempo
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 20245052 16029405 18143081 17397830 17214109 15357363 15394975 16351537
## 2001 23749375 19835413 21431655 20590163 19619234 17653944 17887091 19128329
## 2002 24895852 17809560 19009404 21483428 21504806 19346055 19371622 20883881
## 2003 26293072 20944012 21270059 20297168 20141566 18723700 20257042 22024221
## 2004 29382059 23206328 23459317 22656277 23551298 21900521 22116971 24400017
## 2005 30924056 23802417 24201236 24824711 24794606 23180394 24182569 25083772
## 2006 34993588 28647154 29585898 29249697 28797796 25706759 26033841 26584173
## 2007 36702973 29737047 31686455 28945789 28288791 26726538 26798090 27700348
## 2008 42118581 32228275 31780636 32171007 31930258 29337668 28863041 30468988
## 2009 33894035 26519202 29046303 27846291 28363772 25445202 25112004 27007602
## 2010 40846376 33415513 36027989 33975568 32083570 28238139 27650232 29295633
## 2011 45130021 37357643 38560276 36448273 35404827 31708361 30719600 32592592
## 2012 43426156 37433991 40802950 40082315 37831547 32899677 31910752 34617108
## 2013 50565839 40680959 44406917 42466763 41000509 36435807 35738594 38839169
## 2014 50756539 43321122 45099702 41934604 41747869 36957420 37025913 41152734
## 2015 52649508 39642436 39729938 38418840 41729017 37683077 36270634 40266918
## 2016 52988607 41126314 41853139 38850246 40056076 37254735 36717018 41267090
## 2017 53190888 43003994 46788831 44973129 43046060 37561448 37907959 42006926
## 2018 56124608 44894673 46760478 47233135 46848296 41188930 40135079 44832583
## 2019 59423009 46472295 48108843 45084504 44434465 39733056 38960044 45202489
## 2020 60348396 50808543 51199925 48325135 47516326 42143068
## Sep Oct Nov Dec
## 2000 18480841 24347562 26549262 26625862
## 2001 22182074 28265012 29851910 30319511
## 2002 24019519 27904478 29521250 29632057
## 2003 24901384 30619228 32004914 31847282
## 2004 27066034 33783150 33984572 34257221
## 2005 28603358 36159307 37978500 37751162
## 2006 29950046 37036275 39486415 39935410
## 2007 31487619 40824841 43976913 46020877
## 2008 34497135 43130075 43712398 40755716
## 2009 32435428 40579331 41701336 44130576
## 2010 34922789 44883551 47028624 48415245
## 2011 37204032 46883774 49764919 49254785
## 2012 41449785 52495216 55047056 53439527
## 2013 44722145 56762372 58745294 58035786
## 2014 48891551 58820549 60962665 60787900
## 2015 48640277 59022831 61007316 59472310
## 2016 49636290 59062052 59824556 58693629
## 2017 49503420 60453306 62653021 61990738
## 2018 54334824 64235929 64761722 64918935
## 2019 54730734 67333822 68061032 67111668
## 2020
Se observa que las funciones de acf y pacf estimadas validan los periodos estacionales, porque los coeficientes de la acf para retardos múltiplos del período estacional de la serie, son significativamente distintos de cero. Además la gráfica sirve para obtener candidatos a modelos a probar. Se analiza la existencia de correlaciones significativas, donde los que excedan el IC, son posibles candidatos para el orden de los términos autoregresivos y medias móviles.
2.1: Diferenciación regular y estacional respectivamente, para modelo global.
Usualmente es posible diferenciar la serie original para obtener un proceso estacionario,diferenciando con un lag igual al periodo de estacionalidad, removiendo ambos la componente estacional y la tendencia lineal. El comando diff permite esto. Tomando dos argumentos. El primero, la serie de tiempo la cual se va a diferenciar y el segundo es el lag con el cual se va a diferenciar.
## [1] 1## [1] 12.2: Test ADF (Dickey-Fuller).
Una vez eliminado tanto la componente de tendencia y la estacional,se observas que esta serie se parece bastante a una serie estacionaria, ya que parece ser constante en media y varianza, para asegurarnos aplicamos un test de estacionariedad como el test ADF (Dickey-Fuller) y el test de KPSS (Kwiatkowski-Phillips-Schmidt-Shin).
Contrastamos la hipótesis para un alfa=0.05 H0: La serie no es estacionaria H1: La serie es estacionaria
## Warning in adf.test(pdif): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: pdif
## Dickey-Fuller = -11.365, Lag order = 6, p-value = 0.01
## alternative hypothesis: stationary## [1] 0.01## Warning in kpss.test(pdif): p-value greater than printed p-value##
## KPSS Test for Level Stationarity
##
## data: pdif
## KPSS Level = 0.015355, Truncation lag parameter = 5, p-value = 0.1## [1] 0.1Rechazo H0, la serie no tiene raiz unitaria, es estacionaria
2.3: Modelo en función de una tendencia.
##
## Call:
## lm(formula = quincena2$Suma_KILOSLECHE ~ quincena2$mes)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22015660 -10291977 -479359 8444628 28681483
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30709730 1618498 18.974 < 2e-16 ***
## quincena2$mes 957183 221867 4.314 2.33e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12010000 on 244 degrees of freedom
## Multiple R-squared: 0.07087, Adjusted R-squared: 0.06707
## F-statistic: 18.61 on 1 and 244 DF, p-value: 2.328e-05
2.4: Modelo en función de un Logaritmo
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 16.55 17.11 17.41 17.36 17.62 18.04
2.5: Modelo Cuadrático
##
## Call:
## lm(formula = log.qam ~ +I(time(quincena2$Suma_KILOSLECHE)^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5081 -0.1464 -0.0122 0.1442 0.4495
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.705e+01 2.045e-02 833.88 <2e-16 ***
## I(time(quincena2$Suma_KILOSLECHE)^2) 1.524e-05 7.519e-07 20.27 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2136 on 244 degrees of freedom
## Multiple R-squared: 0.6273, Adjusted R-squared: 0.6258
## F-statistic: 410.8 on 1 and 244 DF, p-value: < 2.2e-16
3: Análisis ARIMA y Wolt-Winters
M(t): = Media del proceso en el instante t. R(t): = Variación de la tendencia respecto de la media en el instante t. E(t):= Estimación del factor estacional en el instante t. s := Período estacional.
3.1: AIC
## Warning in AIC.default(ar1, ma1, arma11, arima010, arima111, arima011,
## arima222, : models are not all fitted to the same number of observations## df AIC
## ar1 3 8243.242
## ma1 3 8471.754
## arma11 4 8190.262
## arima010 1 8212.249
## arima111 3 8158.940
## arima011 2 8164.681
## arima222 5 8134.938
## arima1 4 7221.702
## arima2 4 7222.199
## arima3 7 7199.611
## arima4 6 7220.808
## arima5 6 7200.224
## arima6 3 7220.345
## arima7 3 7245.901
## arima8 6 7199.462
## arima9 5 7219.471
## arima.spss 4 7247.235
## sarima 3 7688.982
## auto 5 7223.0353.2: BIC
## Warning in BIC.default(ar1, ma1, arma11, arima010, arima111, arima011,
## arima222, : models are not all fitted to the same number of observations## df BIC
## ar1 3 8253.758
## ma1 3 8482.270
## arma11 4 8204.283
## arima010 1 8215.750
## arima111 3 8169.444
## arima011 2 8171.683
## arima222 5 8152.424
## arima1 4 7235.506
## arima2 4 7236.003
## arima3 7 7223.768
## arima4 6 7241.514
## arima5 6 7220.930
## arima6 3 7230.698
## arima7 3 7256.254
## arima8 6 7220.168
## arima9 5 7236.726
## arima.spss 4 7261.056
## sarima 3 7699.486
## auto 5 7240.3114: Modelos elegidos para análisis 1 (global), por criterio AIC y cálculo de p-valor a los parámetros.
4.1: Arima8
##
## Call:
## arima(x = qamts, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 0), period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2
## 0.7654 -0.6583 -0.3417 -0.5801 -0.3160
## s.e. 0.0486 0.0651 0.0637 0.0651 0.0648
##
## sigma^2 estimated as 1.4e+12: log likelihood = -3593.73, aic = 7199.46## ar1 ma1 ma2 sar1 sar2
## 0.000000e+00 0.000000e+00 8.000808e-08 0.000000e+00 1.065768e-064.2: Arima3
##
## Call:
## arima(x = qamts, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 1), period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2 sma1
## 0.7609 -0.6530 -0.3470 -0.3028 -0.1909 -0.3115
## s.e. 0.0496 0.0651 0.0633 0.1981 0.1182 0.1984
##
## sigma^2 estimated as 1.386e+12: log likelihood = -3592.81, aic = 7199.61## ar1 ma1 ma2 sar1 sar2 sma1
## 0.000000e+00 0.000000e+00 4.102716e-08 1.263478e-01 1.062604e-01 1.164830e-014.3: Arima5
##
## Call:
## arima(x = qamts, order = c(1, 1, 2), seasonal = list(order = c(1, 1, 1), period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sma1
## 0.7471 -0.6506 -0.3494 -0.0745 -0.5317
## s.e. 0.0503 0.0650 0.0630 0.1014 0.0805
##
## sigma^2 estimated as 1.403e+12: log likelihood = -3594.11, aic = 7200.22## ar1 ma1 ma2 sar1 sma1
## 0.000000e+00 0.000000e+00 2.858804e-08 4.628353e-01 4.075962e-114.4: Box Ljung-Box y Box-Pierce (Test para ruido blanco).
La prueba de Ljung-Box se puede definir de la siguiente manera: H0: Los datos se distribuyen de forma independiente (Los residuos se distribuyen ruido blanco), es decir, las correlaciones en la población de la que se toma la muestra son 0, de modo que cualquier correlación observada en los datos es el resultado de la aleatoriedad del proceso de muestreo. H1: Los datos no se distribuyen de forma independiente (Los residuos NO se distribuyen ruido blanco), lo que implica, que el modelo no es bueno. RECHAZO SI P-VALOR ES MENOR A 0.05
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,2)(2,1,0)[12]
## Q* = 30.481, df = 19, p-value = 0.04599
##
## Model df: 5. Total lags used: 24
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,2)(2,1,1)[12]
## Q* = 29.429, df = 18, p-value = 0.04339
##
## Model df: 6. Total lags used: 24
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,2)(1,1,1)[12]
## Q* = 29.728, df = 19, p-value = 0.05537
##
## Model df: 5. Total lags used: 24Para 2 de los 3 modelos, rechazamos H0, con lo que nos aseguramos que los modelos son buenos, a excepción de Arima5, donde no se rechaza la hipótesis nula.
## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
##
## Call:
## HoltWinters(x = qamts, seasonal = c("multiplicative"))
##
## Smoothing parameters:
## alpha: 0.7627162
## beta : 0
## gamma: 1
##
## Coefficients:
## [,1]
## a 5.386189e+07
## b 2.523507e+05
## s1 7.767417e-01
## s2 8.717921e-01
## s3 1.023973e+00
## s4 1.216356e+00
## s5 1.228655e+00
## s6 1.215152e+00
## s7 1.093123e+00
## s8 8.787320e-01
## s9 9.059761e-01
## s10 8.749589e-01
## s11 8.733907e-01
## s12 7.824283e-01## fit upr lwr
## Min. :42032785 Min. : 44713732 Min. :38041556
## 1st Qu.:52016270 1st Qu.: 61469719 1st Qu.:43284901
## Median :59057386 Median : 70712138 Median :45763430
## Mean :61432670 Mean : 72928664 Mean :49936677
## 3rd Qu.:70661021 3rd Qu.: 82046773 3rd Qu.:60148170
## Max. :86331036 Max. :106998534 Max. :65663538
## Jan Feb Mar Apr May Jun Jul Aug
## 2020 42032785 47396366
## 2021 60808620 49104153 50855199 49334904 49466883 44512424 44384921 50036335
## 2022 64118825 51765136 53598684 51984462 52111693 46881781 46737057 52676304
## 2023 67429030 54426120 56342169 54634021 54756503 49251137 49089193 55316272
## 2024 70739234 57087104 59085654 57283579 57401312 51620494 51441329 57956241
## 2025 74049439 59748088 61829139 59933137 60046122 53989850 53793465 60596210
## Sep Oct Nov Dec
## 2020 55928314 66743004 67727921 67290226
## 2021 59029118 70426383 71448544 70969959
## 2022 62129921 74109762 75169167 74649692
## 2023 65230725 77793140 78889790 78329424
## 2024 68331529 81476519 82610413 82009157
## 2025 71432333 85159898 86331036 85688890
5: Nuevos modelos (Análisis 2, Análisis 3 y Análisis 4)
A1: Serie Real.
A2: 2013 al 2020.
A3: 2013 al 2019.
A4: 2013 al 2018.
6: Modelos ARIMA y Holt-Winters para análisis 2, 3 Y 4.
6.1: Análisis 2 (A2) Holt-Winters
## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
##
## Call:
## HoltWinters(x = qamts.a2, seasonal = c("multiplicative"))
##
## Smoothing parameters:
## alpha: 0.7425349
## beta : 0
## gamma: 1
##
## Coefficients:
## [,1]
## a 5.282571e+07
## b 1.253443e+05
## s1 7.856328e-01
## s2 8.786094e-01
## s3 1.030330e+00
## s4 1.226823e+00
## s5 1.246804e+00
## s6 1.244252e+00
## s7 1.122081e+00
## s8 9.032953e-01
## s9 9.306736e-01
## s10 8.969330e-01
## s11 8.937573e-01
## s12 7.977757e-01## Length Class Mode
## fitted 312 mts numeric
## x 90 ts numeric
## alpha 1 -none- numeric
## beta 1 -none- numeric
## gamma 1 -none- numeric
## coefficients 14 -none- numeric
## seasonal 1 -none- character
## SSE 1 -none- numeric
## call 3 -none- call## Time-Series [1:66, 1:3] from 2020 to 2026: 41600084 46633426 54815343 65422898 66644721 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:3] "fit" "upr" "lwr"## fit upr lwr
## Min. :41600084 Min. :44630257 Min. :33046764
## 1st Qu.:49404886 1st Qu.:59714443 1st Qu.:38470464
## Median :53862391 Median :66877901 Median :41727076
## Mean :57207690 Mean :69917636 Mean :44497744
## 3rd Qu.:66659388 3rd Qu.:79909351 3rd Qu.:53081261
## Max. :76021875 Max. :98828911 Max. :59953741
6.2: Análisis 3 (A3) Holt-Winters
## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
##
## Call:
## HoltWinters(x = qamts.a3, seasonal = c("multiplicative"))
##
## Smoothing parameters:
## alpha: 0.7331678
## beta : 0
## gamma: 1
##
## Coefficients:
## [,1]
## a 5.397014e+07
## b 1.253443e+05
## s1 1.124169e+00
## s2 8.897849e-01
## s3 9.374221e-01
## s4 9.033525e-01
## s5 8.980628e-01
## s6 8.001580e-01
## s7 7.858288e-01
## s8 8.795164e-01
## s9 1.031999e+00
## s10 1.228274e+00
## s11 1.246700e+00
## s12 1.243496e+00## Length Class Mode
## fitted 288 mts numeric
## x 84 ts numeric
## alpha 1 -none- numeric
## beta 1 -none- numeric
## gamma 1 -none- numeric
## coefficients 14 -none- numeric
## seasonal 1 -none- character
## SSE 1 -none- numeric
## call 3 -none- call## Time-Series [1:66, 1:3] from 2020 to 2025: 60812489 48244878 50945309 49206984 49031412 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:3] "fit" "upr" "lwr"## fit upr lwr
## Min. :43100787 Min. :48684545 Min. :33721532
## 1st Qu.:49948650 1st Qu.:60216342 1st Qu.:38903964
## Median :54538330 Median :68772750 Median :41819832
## Mean :57645263 Mean :70570394 Mean :44720133
## 3rd Qu.:67153360 3rd Qu.:78896258 3rd Qu.:52508110
## Max. :76504295 Max. :98771631 Max. :59264313
6.3: Análisis 4 (A4) Holt-Winters
## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
##
## Call:
## HoltWinters(x = qamts.a4, seasonal = c("multiplicative"))
##
## Smoothing parameters:
## alpha: 0.7322216
## beta : 0
## gamma: 1
##
## Coefficients:
## [,1]
## a 5.194620e+07
## b 1.253443e+05
## s1 1.118081e+00
## s2 8.944295e-01
## s3 9.442257e-01
## s4 9.135629e-01
## s5 9.017087e-01
## s6 7.998536e-01
## s7 7.870382e-01
## s8 8.691730e-01
## s9 1.021526e+00
## s10 1.214947e+00
## s11 1.249586e+00
## s12 1.249734e+00## Length Class Mode
## fitted 240 mts numeric
## x 72 ts numeric
## alpha 1 -none- numeric
## beta 1 -none- numeric
## gamma 1 -none- numeric
## coefficients 14 -none- numeric
## seasonal 1 -none- character
## SSE 1 -none- numeric
## call 3 -none- call## Time-Series [1:84, 1:3] from 2019 to 2026: 58220193 46686441 49404000 47914164 47405463 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:3] "fit" "upr" "lwr"## fit upr lwr
## Min. :41574203 Min. : 47185953 Min. :31727129
## 1st Qu.:49156650 1st Qu.: 61067698 1st Qu.:36824013
## Median :54201843 Median : 69625896 Median :40158384
## Mean :57137270 Mean : 71833213 Mean :42441328
## 3rd Qu.:66503852 3rd Qu.: 82186914 3rd Qu.:49985644
## Max. :78077288 Max. :104487636 Max. :56970230
6.4: Modelos seleccionados para análisis 2.
##
## Call:
## arima(x = qamts.a2, order = c(1, 1, 2), seasonal = list(order = c(1, 1, 1),
## period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sma1
## 0.5271 -0.5085 -0.3836 0.2009 -0.9954
## s.e. 0.1431 0.1374 0.1025 0.1499 0.2891
##
## sigma^2 estimated as 1.218e+12: log likelihood = -1191.17, aic = 2394.33
##
## Call:
## arima(x = qamts.a2, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 1),
## period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2 sma1
## 0.5105 -0.5223 -0.3569 0.0855 -0.2327 -0.7990
## s.e. 0.1543 0.1458 0.1154 0.3556 0.2295 0.6451
##
## sigma^2 estimated as 1.271e+12: log likelihood = -1190.37, aic = 2394.75
##
## Call:
## arima(x = qamts.a2, order = c(0, 1, 3), seasonal = list(order = c(2, 1, 0),
## period = 12))
##
## Coefficients:
## ma1 ma2 ma3 sar1 sar2
## 0.0187 -0.4167 -0.353 -0.4569 -0.3931
## s.e. 0.1203 0.0909 0.113 0.1217 0.1347
##
## sigma^2 estimated as 1.478e+12: log likelihood = -1191.41, aic = 2394.82
6.5: Modelos seleccionados para análisis 3.
##
## Call:
## arima(x = qamts.a3, order = c(0, 1, 3), seasonal = list(order = c(2, 1, 0),
## period = 12))
##
## Coefficients:
## ma1 ma2 ma3 sar1 sar2
## 0.0527 -0.4389 -0.3611 -0.4037 -0.4151
## s.e. 0.1143 0.1046 0.1207 0.1337 0.1357
##
## sigma^2 estimated as 1.429e+12: log likelihood = -1097.73, aic = 2207.46
##
## Call:
## arima(x = qamts.a3, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 0),
## period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2
## 0.4782 -0.4527 -0.4229 -0.4056 -0.4385
## s.e. 0.1537 0.1442 0.1136 0.1313 0.1317
##
## sigma^2 estimated as 1.44e+12: log likelihood = -1098.26, aic = 2208.53
##
## Call:
## arima(x = qamts.a3, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 1),
## period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2 sma1
## 0.4669 -0.4548 -0.4139 -0.0583 -0.3522 -0.4733
## s.e. 0.1568 0.1478 0.1141 0.2968 0.1751 0.3493
##
## sigma^2 estimated as 1.351e+12: log likelihood = -1097.29, aic = 2208.58
6.6: Modelos seleccionados para análisis 4.
## Series: qamts.a4
## ARIMA(0,1,3)(2,1,0)[12]
##
## Coefficients:
## ma1 ma2 ma3 sar1 sar2
## 0.1411 -0.469 -0.3870 -0.2797 -0.4143
## s.e. 0.1424 0.107 0.1528 0.1474 0.1672
##
## sigma^2 estimated as 1.476e+12: log likelihood=-910.8
## AIC=1833.59 AICc=1835.21 BIC=1846.06
##
## Call:
## arima(x = qamts.a4, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 1),
## period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2 sma1
## 0.3032 -0.3327 -0.4672 0.0651 -0.4587 -0.6940
## s.e. 0.1922 0.1599 0.1137 0.2414 0.1800 0.4934
##
## sigma^2 estimated as 1.09e+12: log likelihood = -910.41, aic = 1834.81
##
## Call:
## arima(x = qamts.a4, order = c(1, 1, 2), seasonal = list(order = c(2, 1, 0),
## period = 12))
##
## Coefficients:
## ar1 ma1 ma2 sar1 sar2
## 0.3488 -0.3473 -0.4683 -0.3099 -0.4837
## s.e. 0.1814 0.1499 0.1096 0.1414 0.1489
##
## sigma^2 estimated as 1.375e+12: log likelihood = -912.18, aic = 1836.36
7: MPE(error porcentual medio) para Análisis 3: (BackTest)
## qamts quincena2$mes quincena2$año mpe.3.1.arimaex mpe.3.2.arima8
## [1,] 59423009 1 2019 NA NA
## [2,] 46472295 2 2019 NA NA
## [3,] 48108843 3 2019 NA NA
## [4,] 45084504 4 2019 NA NA
## [5,] 44434465 5 2019 NA NA
## [6,] 39733056 6 2019 NA NA
## [7,] 38960044 7 2019 NA NA
## [8,] 45202489 8 2019 NA NA
## [9,] 54730734 9 2019 NA NA
## [10,] 67333822 10 2019 NA NA
## [11,] 68061032 11 2019 NA NA
## [12,] 67111668 12 2019 NA NA
## [13,] 60348396 1 2020 -0.002767392 -0.011430967
## [14,] 50808543 2 2020 0.047539849 0.041776104
## [15,] 51199925 3 2020 0.009485905 0.004085338
## [16,] 48325135 4 2020 0.003585015 0.001475838
## [17,] 47516326 5 2020 0.011522871 0.011411073
## [18,] 42143068 6 2020 0.004505633 0.005015400
## mpe.3.3.arima3 mpe.3.4.hw
## [1,] NA NA
## [2,] NA NA
## [3,] NA NA
## [4,] NA NA
## [5,] NA NA
## [6,] NA NA
## [7,] NA NA
## [8,] NA NA
## [9,] NA NA
## [10,] NA NA
## [11,] NA NA
## [12,] NA NA
## [13,] -0.0051959865 -0.007690230
## [14,] 0.0494737208 0.050457367
## [15,] 0.0211557816 0.004972981
## [16,] 0.0222894225 -0.018248238
## [17,] 0.0173619456 -0.031885593
## [18,] 0.0005585556 -0.038994416## qamts quincena2$mes quincena2$año mpe.3.1.arimaex
## Min. :38960044 Min. : 1.00 Min. :2019 Min. :-0.002767
## 1st Qu.:45114000 1st Qu.: 3.00 1st Qu.:2019 1st Qu.: 0.003815
## Median :48216989 Median : 5.00 Median :2019 Median : 0.006996
## Mean :51388742 Mean : 5.50 Mean :2019 Mean : 0.012312
## 3rd Qu.:58249940 3rd Qu.: 7.75 3rd Qu.:2020 3rd Qu.: 0.011014
## Max. :68061032 Max. :12.00 Max. :2020 Max. : 0.047540
## NA's :12
## mpe.3.2.arima8 mpe.3.3.arima3 mpe.3.4.hw
## Min. :-0.011431 Min. :-0.005196 Min. :-0.038994
## 1st Qu.: 0.002128 1st Qu.: 0.004759 1st Qu.:-0.028476
## Median : 0.004550 Median : 0.019259 Median :-0.012969
## Mean : 0.008722 Mean : 0.017607 Mean :-0.006898
## 3rd Qu.: 0.009812 3rd Qu.: 0.022006 3rd Qu.: 0.001807
## Max. : 0.041776 Max. : 0.049474 Max. : 0.050457
## NA's :12 NA's :12 NA's :12Observar las medias de cada modelo y notar que el MPE que más se acerca a Cero es Arima8
8: MPE(error porcentual medio) para Análisis 4: (BackTest)
## qamts quincena2$mes quincena2$año mpe.4.1.arima.auto mpe.4.2.arima3
## [1,] 59423009 1 2019 -0.001931389 0.0202082172
## [2,] 46472295 2 2019 -0.020187429 -0.0003219129
## [3,] 48108843 3 2019 0.002434561 0.0183495509
## [4,] 45084504 4 2019 -0.049863434 -0.0162261936
## [5,] 44434465 5 2019 -0.076062523 -0.0597290503
## [6,] 39733056 6 2019 -0.090159163 -0.0813192030
## [7,] 38960044 7 2019 -0.085390027 -0.0744386261
## [8,] 45202489 8 2019 -0.039850469 -0.0216590175
## [9,] 54730734 9 2019 -0.028793953 -0.0008896676
## [10,] 67333822 10 2019 0.021744552 0.0392193269
## [11,] 68061032 11 2019 0.026341000 0.0348333983
## [12,] 67111668 12 2019 0.016532927 0.0303863188
## [13,] 60348396 1 2020 -0.004763473 0.0341634480
## [14,] 50808543 2 2020 0.031824065 0.0702832391
## [15,] 51199925 3 2020 0.005328340 0.0457768713
## [16,] 48325135 4 2020 -0.027136627 0.0419901292
## [17,] 47516326 5 2020 -0.036211638 0.0113820101
## [18,] 42143068 6 2020 -0.055592533 -0.0211220878
## mpe.4.3.arima8 mpe.4.4.hw
## [1,] 0.005791765 0.020241595
## [2,] -0.009630369 -0.004608029
## [3,] 0.007517945 -0.026921399
## [4,] -0.039883516 -0.062763468
## [5,] -0.069358051 -0.066862458
## [6,] -0.087316751 -0.060852223
## [7,] -0.081944674 -0.067098463
## [8,] -0.037155423 -0.018125450
## [9,] -0.026561211 0.009390599
## [10,] 0.024660668 0.040085219
## [11,] 0.029948102 0.020964414
## [12,] 0.021045223 0.004663396
## [13,] 0.005327613 0.007398086
## [14,] 0.042281132 0.054651486
## [15,] 0.009028940 0.007337602
## [16,] -0.017704930 -0.019930579
## [17,] -0.026023115 -0.026210471
## [18,] -0.046588733 -0.028733506## qamts quincena2$mes quincena2$año mpe.4.1.arima.auto
## Min. :38960044 Min. : 1.00 Min. :2019 Min. :-0.090159
## 1st Qu.:45114000 1st Qu.: 3.00 1st Qu.:2019 1st Qu.:-0.047360
## Median :48216989 Median : 5.00 Median :2019 Median :-0.023662
## Mean :51388742 Mean : 5.50 Mean :2019 Mean :-0.022874
## 3rd Qu.:58249940 3rd Qu.: 7.75 3rd Qu.:2020 3rd Qu.: 0.004605
## Max. :68061032 Max. :12.00 Max. :2020 Max. : 0.031824
## mpe.4.2.arima3 mpe.4.3.arima8 mpe.4.4.hw
## Min. :-0.081319 Min. :-0.087317 Min. :-0.067098
## 1st Qu.:-0.019898 1st Qu.:-0.039201 1st Qu.:-0.028280
## Median : 0.014866 Median :-0.013668 Median :-0.011367
## Mean : 0.003938 Mean :-0.016476 Mean :-0.012076
## 3rd Qu.: 0.034666 3rd Qu.: 0.008651 3rd Qu.: 0.008892
## Max. : 0.070283 Max. : 0.042281 Max. : 0.054651Observar las medias de cada modelo y notar que el MPE que más se acerca a Cero es Arima3.
9: MAPE(error porcentual absoluto medio) para Análisis 3: (BackTest)
## qamts quincena2$mes quincena2$año mape.3.1.arimaex mape.3.2.arima8
## [1,] 59423009 1 2019 NA NA
## [2,] 46472295 2 2019 NA NA
## [3,] 48108843 3 2019 NA NA
## [4,] 45084504 4 2019 NA NA
## [5,] 44434465 5 2019 NA NA
## [6,] 39733056 6 2019 NA NA
## [7,] 38960044 7 2019 NA NA
## [8,] 45202489 8 2019 NA NA
## [9,] 54730734 9 2019 NA NA
## [10,] 67333822 10 2019 NA NA
## [11,] 68061032 11 2019 NA NA
## [12,] 67111668 12 2019 NA NA
## [13,] 60348396 1 2020 0.2767392 1.1430967
## [14,] 50808543 2 2020 4.7539849 4.1776104
## [15,] 51199925 3 2020 0.9485905 0.4085338
## [16,] 48325135 4 2020 0.3585015 0.1475838
## [17,] 47516326 5 2020 1.1522871 1.1411073
## [18,] 42143068 6 2020 0.4505633 0.5015400
## mape.3.3.arima3 mape.3.4.hw
## [1,] NA NA
## [2,] NA NA
## [3,] NA NA
## [4,] NA NA
## [5,] NA NA
## [6,] NA NA
## [7,] NA NA
## [8,] NA NA
## [9,] NA NA
## [10,] NA NA
## [11,] NA NA
## [12,] NA NA
## [13,] 0.51959865 0.7690230
## [14,] 4.94737208 5.0457367
## [15,] 2.11557816 0.4972981
## [16,] 2.22894225 1.8248238
## [17,] 1.73619456 3.1885593
## [18,] 0.05585556 3.8994416## qamts quincena2$mes quincena2$año mape.3.1.arimaex
## Min. :38960044 Min. : 1.00 Min. :2019 Min. :0.2767
## 1st Qu.:45114000 1st Qu.: 3.00 1st Qu.:2019 1st Qu.:0.3815
## Median :48216989 Median : 5.00 Median :2019 Median :0.6996
## Mean :51388742 Mean : 5.50 Mean :2019 Mean :1.3234
## 3rd Qu.:58249940 3rd Qu.: 7.75 3rd Qu.:2020 3rd Qu.:1.1014
## Max. :68061032 Max. :12.00 Max. :2020 Max. :4.7540
## NA's :12
## mape.3.2.arima8 mape.3.3.arima3 mape.3.4.hw
## Min. :0.1476 Min. :0.05586 Min. :0.4973
## 1st Qu.:0.4318 1st Qu.:0.82375 1st Qu.:1.0330
## Median :0.8213 Median :1.92589 Median :2.5067
## Mean :1.2532 Mean :1.93392 Mean :2.5375
## 3rd Qu.:1.1426 3rd Qu.:2.20060 3rd Qu.:3.7217
## Max. :4.1776 Max. :4.94737 Max. :5.0457
## NA's :12 NA's :12 NA's :1210: MAPE(error porcentual absoluto medio) para Análisis 4: (BackTest)
## qamts quincena2$mes quincena2$año mape.4.1.arima.auto mape.4.2.arima3
## [1,] 59423009 1 2019 0.1931389 2.02082172
## [2,] 46472295 2 2019 2.0187429 0.03219129
## [3,] 48108843 3 2019 0.2434561 1.83495509
## [4,] 45084504 4 2019 4.9863434 1.62261936
## [5,] 44434465 5 2019 7.6062523 5.97290503
## [6,] 39733056 6 2019 9.0159163 8.13192030
## [7,] 38960044 7 2019 8.5390027 7.44386261
## [8,] 45202489 8 2019 3.9850469 2.16590175
## [9,] 54730734 9 2019 2.8793953 0.08896676
## [10,] 67333822 10 2019 2.1744552 3.92193269
## [11,] 68061032 11 2019 2.6341000 3.48333983
## [12,] 67111668 12 2019 1.6532927 3.03863188
## [13,] 60348396 1 2020 0.4763473 3.41634480
## [14,] 50808543 2 2020 3.1824065 7.02832391
## [15,] 51199925 3 2020 0.5328340 4.57768713
## [16,] 48325135 4 2020 2.7136627 4.19901292
## [17,] 47516326 5 2020 3.6211638 1.13820101
## [18,] 42143068 6 2020 5.5592533 2.11220878
## mape.4.3.arima8 mape.4.4.hw
## [1,] 0.5791765 2.0241595
## [2,] 0.9630369 0.4608029
## [3,] 0.7517945 2.6921399
## [4,] 3.9883516 6.2763468
## [5,] 6.9358051 6.6862458
## [6,] 8.7316751 6.0852223
## [7,] 8.1944674 6.7098463
## [8,] 3.7155423 1.8125450
## [9,] 2.6561211 0.9390599
## [10,] 2.4660668 4.0085219
## [11,] 2.9948102 2.0964414
## [12,] 2.1045223 0.4663396
## [13,] 0.5327613 0.7398086
## [14,] 4.2281132 5.4651486
## [15,] 0.9028940 0.7337602
## [16,] 1.7704930 1.9930579
## [17,] 2.6023115 2.6210471
## [18,] 4.6588733 2.8733506## qamts quincena2$mes quincena2$año mape.4.1.arima.auto
## Min. :38960044 Min. : 1.00 Min. :2019 Min. :0.1931
## 1st Qu.:45114000 1st Qu.: 3.00 1st Qu.:2019 1st Qu.:1.7447
## Median :48216989 Median : 5.00 Median :2019 Median :2.7965
## Mean :51388742 Mean : 5.50 Mean :2019 Mean :3.4453
## 3rd Qu.:58249940 3rd Qu.: 7.75 3rd Qu.:2020 3rd Qu.:4.7360
## Max. :68061032 Max. :12.00 Max. :2020 Max. :9.0159
## mape.4.2.arima3 mape.4.3.arima8 mape.4.4.hw
## Min. :0.03219 Min. :0.5328 Min. :0.4608
## 1st Qu.:1.88142 1st Qu.:1.1649 1st Qu.:1.1574
## Median :3.22749 Median :2.6292 Median :2.3587
## Mean :3.45721 Mean :3.2654 Mean :3.0380
## 3rd Qu.:4.48302 3rd Qu.:4.1682 3rd Qu.:5.1010
## Max. :8.13192 Max. :8.7317 Max. :6.7098