corrected ARMA(p,q) to ARIMA(p,d,q)

Author: englianhu

Q1App2/app.R

@@ -199,7 +199,11 @@ ui <- shinyUI(fluidPage(
                               tags$a(href='https://github.com/scibrokes/owner', target='_blank', 
                                      tags$img(height = '20px', alt='hot', #align='right', 
                                               src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/www/hot.jpg'))), 
-                            p('02. ', HTML("<a href='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/Successful%20Algorithmic%20Trading.pdf'>A Step-by-Step Guide to Quantitative Strategies - SUCCESSFUL ALGORITHMIC TRADING</a>"), 
+                            p('02. ', HTML("<a href='https://systematicinvestor.wordpress.com/shiny/'>Shiny App in Systematic Investor Toolbox (SIT)</a>"), 
+                              tags$a(href='https://github.com/scibrokes/owner', target='_blank', 
+                                     tags$img(height = '20px', alt='hot', #align='right', 
+                                              src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/www/hot.jpg'))), 
+                            p('03. ', HTML("<a href='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/Successful%20Algorithmic%20Trading.pdf'>A Step-by-Step Guide to Quantitative Strategies - SUCCESSFUL ALGORITHMIC TRADING</a>"), 
                               tags$a(href='https://github.com/scibrokes/owner', target='_blank', 
                                      tags$img(height = '20px', alt='hot', #align='right', 
                                               src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/www/hot.jpg')))), 

README.html

@@ -55,6 +55,10 @@ In order to test the timeline of daily highest and lowest price, here I created
 
 *binary.com Interview Question I - Tick-Data-HiLo For Daily Trading (Blooper)* descript that the VaR figure required in order to place orders. [What is the difference between Sharpe ratio and value at risk?](https://www.quora.com/What-is-the-difference-between-Sharpe-ratio-and-value-at-risk) states the difference between VaR and shape ratio where the shape ratio will be use in the future research.
 
+[ARIMA+GARCH Trading Strategy on the S&P500 Stock Market Index Using R](https://www.quantstart.com/articles/ARIMA-GARCH-Trading-Strategy-on-the-SP500-Stock-Market-Index-Using-R) compares the ROI of buy and hold and application of ARIMA + GARCH model.
+
+[Systematic Investor Blog : Trading Strategies](https://systematicinvestor.wordpress.com/category/trading-strategies/) introduce various trading strategies.
+
 ## Intro Reference
 
 *Currency Hedging Strategies Using Dynamic Multivariate GARCH* compares DCC, BEKK, CCC and VARMA-AGARCH models to examine the conditional volatilities among the spot and two distint futures maturities, namely near-month and next-to-near-month contracts. The estimated conditionl covariances matrices from these models were used to calculate the optimal portfolios weights and optimal hedge ratios. The empirical results in the paper reveal that there are not big differences either the near-month or next-to-near-month contract is used for hedge spot position on currencies. They also reveal that hedging ratios are lower for near-month contract when the USD/EUR and USD/JPY exchange rates are anlyzed. This result is explained in terms of the higher correlation between spot prices and the next-to-near-month future prices than that with near-month contract and additionally because of the lower volatility of the long maturity futures. Finally across all currencies and error densities, the CCC and VARMA-AGARCH models provide similar results in terms of hedging ratios, portfolio variance reduction and hedging effectiveness. Some difference might appear when the DCC and BEKK models are used. Below is the table summary of the paper.

README.md

@@ -1,6 +1,6 @@
 ---
 title: "<img src='www/binary-logo-resize.jpg' width='240'>"
-subtitle: "[binary.com](https://github.com/englianhu/binary.com-interview-question) 面试试题 I - GARCH模型中的`ARMA(p,d,q)`参数最优化"
+subtitle: "[binary.com](https://github.com/englianhu/binary.com-interview-question) 面试试题 I - GARCH模型中的`ARIMA(p,d,q)`参数最优化"
 author: "[<span style='color:blue'>®γσ, Lian Hu</span>](https://englianhu.github.io/) <img src='www/ENG.jpg' width='24'> <img src='www/RYO.jpg' width='24'>®"
 date: "`r lubridate::today('Asia/Tokyo')`"
 output:
@@ -724,6 +724,15 @@ acc %>%
 
 结果新的Fi-gjrGARCH函数pred2胜出，比旧的gjrGARCH的pred1更优秀，证明`p`值、`d`值与`q`值仨都可以优化。目前正在编写着[Q1App2](https://beta.rstudioconnect.com/content/3138/)自动交易应用。“商场如战场”，除了模式最优化以外，程序运作上分秒必争... `microbenchmark`测试效率，之前编写了个[DataCollection](https://beta.rstudioconnect.com/content/3153/)应用采集实时数据以方便之后的高频率交易自动化建模^[不过数据量多就会当机，得继续提升才行。]。欲知更多详情，请参阅[Real Time FXCM](https://github.com/scibrokes/real-time-fxcm)。
 
+[Generalised Autoregressive Conditional Heteroskedasticity GARCH(p, q) Models for Time Series Analysis](https://www.quantstart.com/articles/Generalised-Autoregressive-Conditional-Heteroskedasticity-GARCH-p-q-Models-for-Time-Series-Analysis): 
+
+- [Discrete White Noise and Random Walks](https://www.quantstart.com/articles/White-Noise-and-Random-Walks-in-Time-Series-Analysis)
+- [AR(p)](https://www.quantstart.com/articles/Autoregressive-Moving-Average-ARMA-p-q-Models-for-Time-Series-Analysis-Part-1)
+- [MA(q)](https://www.quantstart.com/articles/Autoregressive-Moving-Average-ARMA-p-q-Models-for-Time-Series-Analysis-Part-2)
+- [ARMA(p,q)](https://www.quantstart.com/articles/Autoregressive-Moving-Average-ARMA-p-q-Models-for-Time-Series-Analysis-Part-3)
+- [ARIMA(p,d,q)](https://www.quantstart.com/articles/Autoregressive-Integrated-Moving-Average-ARIMA-p-d-q-Models-for-Time-Series-Analysis)
+
+
 **投注模式**
 
 ![](www/fractional-kelly.jpg)

binary-Q1BET.Rmd

@@ -31,13 +31,15 @@ rm(pkgs)
 
 # Introduction
 
-From previous papers, I tried to apply few models for FOREX price forecasting and eventually got to know <span style='color:red'>Fractional Intergrated GJR-GARCH</span> is the best fit model as we can refer to [GARCH模型中的ARMA(p,d,q)参数最优化](http://rpubs.com/englianhu/binary-Q1FiGJRGARCH). Today I am zooming into the multivariate GARCH models.
+From previous papers, I tried to apply few models for FOREX price forecasting and eventually got to know <span style='color:red'>Fractional Intergrated GJR-GARCH</span> is the best fit model as we can refer to [GARCH模型中的ARIMA(p,d,q)参数最优化](http://rpubs.com/englianhu/binary-Q1FiGJRGARCH). **The standalone ARFIMAX model and methods** in the [A short introduction to the rugarch package](http://www.unstarched.net/r-examples/rugarch/a-short-introduction-to-the-rugarch-package/) describe the `autoarfima()` function where we can easily get the optimal MA and AR figure. [](https://stats.stackexchange.com/questions/176550/fitting-arima-garch-model-using-rugarch-package?answertab=votes#tab-top).
+
+Today I am zooming into the multivariate GARCH models.
 
 # Data
 
 ## Read Data
 
-Similar with *GARCH模型中的ARMA(p,d,q)参数最优化*, I use the dataset from [Binary-Q1 (Extention)](http://rpubs.com/englianhu/binary-Q1E).
+Similar with *GARCH模型中的ARIMA(p,d,q)参数最优化*, I use the dataset from [Binary-Q1 (Extention)](http://rpubs.com/englianhu/binary-Q1E).
 
 ```{r read-data, warning=FALSE}
 cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X', 
@@ -482,6 +484,11 @@ Above models set `VAR=TRUE` and `robust=FALSE`, now I based on above best fitted
 
 ```
 
+### Hi-Lo
+
+### Hi-Lo-Cl
+
+### Cl
 
 ## GO-GARCH
 
@@ -512,44 +519,34 @@ names(attributes(attributes(attributes(fit)$mfit$ufit)[[1]][[3]])$fit)
 
 ## BEKK
 
-[[问答] 向各位朋友求助关于MGARCH-BEKK模型的问题！万分感谢！](http://bbs.pinggu.org/forum.php?mod=viewthread&tid=2263348)
+[[问答] 向各位朋友求助关于MGARCH-BEKK模型的问题！万分感谢！](http://bbs.pinggu.org/forum.php?mod=viewthread&tid=2263348) discuss about the BEKK model.
 
-# Model Comparison
+```{r}
+if (!((method == "Nelder-Mead") || (method == "BFGS") || 
+        (method == "CG") || (method == "L-BFGS-B") || (method == 
+        "SANN"))) {
+        stop("'", method, "' method is not available")
+    }
+```
+
+## mGJR (Bivariate GJR (bivariate asymmetric GARCH model))
 
-```{r tidy-data1}
-##数据1
-fx1 <- llply(names(cr_code), function(x) {
-    fls <- list.files(paste0('data/fx/', x), pattern = '^pred1')
-    dfm <- ldply(fls, function(y) {
-        readRDS(paste0('data/fx/', x, '/', y))
-    }) %>% data.frame(Cat = 'pred1', .) %>% tbl_df
-    names(dfm)[4:5] <- c('Price', 'Price.T1')
-    dfm
- })
-names(fx1) <- names(cr_code)
-
-##数据2
-fx2 <- llply(names(cr_code), function(x) {
-    fls <- list.files(paste0('data/fx/', x), pattern = '^pred2')
-    dfm <- ldply(fls, function(y) {
-        readRDS(paste0('data/fx/', x, '/', y))
-    }) %>% data.frame(Cat = 'pred2', .) %>% tbl_df
-    names(dfm)[4:5] <- c('Price', 'Price.T1')
-    dfm
- })
-names(fx2) <- names(cr_code)
-
-## Merge and tidy dataset.
-fx1 %<>% ldply %>% tbl_df
-fx2 %<>% ldply %>% tbl_df
-fx <- suppressAll(
-  bind_rows(fx1, fx2) %>% arrange(Date) %>% 
-    mutate(.id = factor(.id), Cat = factor(Cat), Price.T1 = lag(Price.T1, 56)) %>% 
-    dplyr::filter(Date >= ymd('2013-01-01') & Date <= ymd('2017-08-30')))
-
-rm(fx1, fx2)
+`mGJR(eps1, eps2, order = c(1, 1, 1), params = NULL, fixed = NULL, method = "BFGS")`
+
+```{r, eval=FALSE}
+if (!((method == "Nelder-Mead") || (method == "BFGS") || 
+        (method == "CG") || (method == "L-BFGS-B") || (method == 
+        "SANN"))) {
+        stop("'", method, "' method is not available")
+    }
 ```
 
+The `mGJR()` function in `mgarchBEKK` use diversified optim function.
+
+
+
+# Model Comparison
+
 # Conclusion
 
 
@@ -604,7 +601,7 @@ rm(sys1, sys2)
 
 01. [Betting Strategy and Model Validation - Part II](https://englianhu.github.io/2017/10/Betting_Strategy_and_Model_Validation_-_Part_02/)
 02. [**binary.com Job Application - Quantitative Analyst** *sample question*](https://github.com/englianhu/binary.com-interview-question)
-03. [GARCH模型中的`ARMA(p,d,q)`参数最优化](http://rpubs.com/englianhu/binary-Q1FiGJRGARCH)
+03. [GARCH模型中的`ARIMA(p,d,q)`参数最优化](http://rpubs.com/englianhu/binary-Q1FiGJRGARCH)
 04. [The `rmgarch` Models - Background and Properties](https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/The%20rmgarch%20Models%20-%20Background%20and%20Properties.pdf)
 05. [Financial Econometrics Practical - Univariate Volatility Modelling](https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/Financial%20Econometrics%20Practical%20-%20Univariate%20Volatility%20Modelling.pdf)
 06. [The GARCH-DCC Model and 2-Stage DCC(MVT) Estimation](http://www.unstarched.net/2013/01/03/the-garch-dcc-model-and-2-stage-dccmvt-estimation/)
@@ -635,6 +632,7 @@ rm(sys1, sys2)
 18. [Forecasting the Daily Dynamic Hedge Ratios by GARCH Models - Evidence from the Agricultural Futures Markets](https://github.com/englianhu/binary.com-interview-question/blob/master/reference/Forecasting%20the%20Daily%20Dynamic%20Hedge%20Ratios%20by%20GARCH%20Models%20-%20Evidence%20from%20the%20Agricultural%20Futures%20Markets.pdf)
 19. [Currency Hedging Strategies Using Dynamic Multivariate GARCH](https://github.com/englianhu/binary.com-interview-question/blob/master/reference/Currency%20Hedging%20Strategies%20Using%20Dynamic%20Multivariate%20GARCH.pdf)
 20. [Multivariate DCC-GARCH Model](https://github.com/englianhu/binary.com-interview-question/blob/master/reference/Multivariate%20DCC-GARCH%20Model.pdf)
+21. [Introduction to the `rugarch` Package](https://github.com/englianhu/binary.com-interview-question/blob/master/reference/Introduction%20to%20the%20rugarch%20Package.pdf)
 
 ---