{"id":18731,"date":"2024-02-26T00:00:00","date_gmt":"2024-02-26T00:00:00","guid":{"rendered":"https:\/\/thierrymoudiki.github.io\/\/blog\/2024\/02\/26\/python\/r\/julia\/ahead-v0100"},"modified":"2024-02-26T00:00:00","modified_gmt":"2024-02-26T00:00:00","slug":"ahead-forecasting-v0-10-0-fast-time-series-model-calibration-and-python-plots","status":"publish","type":"post","link":"https:\/\/python-bloggers.com\/2024\/02\/ahead-forecasting-v0-10-0-fast-time-series-model-calibration-and-python-plots\/","title":{"rendered":"ahead forecasting (v0.10.0): fast time series model calibration and Python plots"},"content":{"rendered":"
\r\nThis article was first published on \r\n T. Moudiki's Webpage - Python <\/a><\/strong>, and kindly contributed to python-bloggers<\/a>. (You can report issue about the content on this page here<\/a>)\r\nWant to share your content on python-bloggers? click here<\/a>.<\/i>\r\n<\/div>\n

ahead<\/code> is an R<\/a>, Python<\/a> and Julia<\/a> package for univariate and multivariate time series forecasting with uncertainty quantification<\/strong> (including predictive simulation). Matlab<\/a> is next. The aim is always to make these implementations of ahead<\/code> as similar as possible<\/strong>, but that\u2019s a looot of work as you might guess. Do not hesitate to submit a pull request<\/a> to these repositories if you want to help and contribute. You can also signal bugs (constructively)<\/a>.<\/p>\n

The main changes in ahead<\/code>\u2019s v0.10.0<\/code> are:<\/p>\n

    \n
  1. Fast calibration<\/strong> of ridge2f<\/code><\/a> using a Leave-One-Out Cross-Validation<\/a> (LOOCV) trick (R for now)<\/li>\n
  2. Univariate forecasting<\/strong> with ridge2f<\/code> with external regressors<\/li>\n
  3. Plotting functionality<\/strong> in Python version<\/li>\n<\/ol>\n

    Read on for more details. You can also use this notebook<\/a> if you want to reproduce the experiments.<\/p>\n

    1. Fast calibration of ridge2f<\/code>:<\/strong><\/h1>\n

    The fast calibration of ridge2f<\/code> uses a remarkable result available for linear models\u2019 LOOCV:<\/p>\n

    \\[LOOCV error = \\frac{1}{n} \\sum_{i=1}^n\\left(y_i-\\hat{f}_{-i}\\left(\\mathbf{z}_i\\right)\\right)^2 = \\frac{1}{n} \\sum_{i=1}^n\\left(\\frac{y_i-\\hat{f}\\left(\\mathbf{z}_i\\right)}{1-\\mathbf{S}_{i i}}\\right)^2\\]<\/p>\n

    Where \\(\\hat{f}_{-i}\\left(\\mathbf{z}_i\\right)\\) is a model statistical learning model $f$ fitted without the \\(i\\)-th observation, \\(\\mathbf{z}_i\\) is the \\(i\\)-th observation, and \\(\\mathbf{S}_{i i}\\) is the $i$-th diagonal element of the hat matrix (a.k.a smoother, a matrix so that \\(\\hat{y} = \\mathbf{S} y\\)). LOOCV is valid for time series<\/a> data<\/strong> because contrary to other cross-validation<\/a> techniques, it does not break the sequential structure of the inputs. Keep in mind<\/strong>, however, that time series cross-vaidation<\/a> will give different results.<\/p>\n

    The LOOCV result can be extended further and approximated by Generalized Cross-Validation (GCV)<\/a>, still with a closed-form formula available. GCV is used in ahead::ridge2f<\/code>. Indeed, even though ridge2<\/code> is not \u2013 strictly speaking \u2013 linear, it possesses the structure of a ridge regression<\/a> model with 2 regularization parameters<\/a>; a regularization parameter for the original explanative variables, and a regularization parameter for new, engineered features. These engineered features transform the linear model into a non-linear one.<\/p>\n

    In the following R example, it\u2019s worth mentioning that only the 2 regularization parameters are calibrated<\/strong>. Other hyperparameters such as the number of time series lags or the number of nodes in the hidden layer are set to their default values. Feel free try and share other experiments including them.<\/p>\n

    %load_ext rpy2.ipython\n<\/pre>\n
    %%R\n\noptions(repos = c(\n    techtonique = 'https:\/\/techtonique.r-universe.dev',\n    CRAN = 'https:\/\/cloud.r-project.org'))\n\ninstall.packages(\"ahead\")\ninstall.packages(\"ggplot2\")\ninstall.packages(\"forecast\")\ninstall.packages(\"dfoptim\")\n<\/pre>\n
    %%R\n\nlibrary(ahead)\nlibrary(dfoptim)\n<\/pre>\n
    # Convert to R DataFrame\n%R -i df\n<\/pre>\n
    %R df_ts <- as.ts(df)\n<\/pre>\n
    %%R\n\nobjective_function <- function(xx)\n{\n    ahead::loocvridge2f(df_ts,\n                        h = 20,\n                        type_pi=\"blockbootstrap\",\n                        lambda_1=10^xx[1],\n                        lambda_2=10^xx[2],\n                        show_progress = FALSE,\n                        )$loocv\n}\nstart <- proc.time()[3]\n(opt <- dfoptim::nmkb(fn=objective_function, lower=c(-10,-10), upper=c(10,10), par=c(0.1, 0.1)))\nprint(proc.time()[3]-start)\n<\/pre>\n
    elapsed \n  6.657 \n<\/pre>\n
    %%R\n\nstart <- proc.time()[3]\nres <- ahead::ridge2f(df_ts, h = 20,\n                      type_pi=\"blockbootstrap\",\n                      lambda_1=10^opt$par[1], # 'optimal' parameters\n                      lambda_2=10^opt$par[2]) # 'optimal' parameters\nprint(proc.time()[3]-start)\n<\/pre>\n
      |======================================================================| 100%\nelapsed \n  0.805 \n<\/pre>\n
    %%R\n\npar(mfrow=c(2, 2))\nplot(res, \"realgovt\", type = \"sims\", main=\"50 predictive simulations \\n of realgovt\")\nplot(res, \"realgovt\", type = \"dist\", main=\"predictive distribution \\n of realgovt\")\nplot(res, \"realgdp\", type = \"sims\", main=\"50 predictive simulations \\n of realgdp\")\nplot(res, \"realgdp\", type = \"dist\", main=\"predictive distribution \\n of realgovt\")\n<\/pre>\n
    \"xxx\"<\/p>\n
    2. Univariate forecasting with ridge2f<\/code> with external regressors:<\/strong><\/h1>\n
    ridge2f<\/code> was initially designed for multivariate time series forecasting. Nothing prevents it from being used for univariate forecasting. This functionality is now available in ahead<\/code> (R for now). In addition, as in the multivariate case, it is possible to use external regressors in the forecasting process.<\/p>\n
    %%R\n\nlibrary(ggplot2)\nlibrary(forecast)\n\nx <- fdeaths\nxreg <- ahead::createtrendseason(x)\n(z <- ahead::ridge2f(x, xreg = xreg, h=20))\nautoplot(z)\n<\/pre>\n
    \"xxx\"<\/p>\n
    3. Plotting functionality in Python version:<\/strong><\/h1>\n
    Install and import packages<\/strong><\/p>\n
    !pip install ahead\n<\/pre>\n
    import numpy as np\nimport pandas as pd\nimport statsmodels.api as sm\n\nfrom time import time\nfrom ahead import Ridge2Regressor # may take some time to run, ONLY the 1st time it's run\nfrom statsmodels.tsa.base.datetools import dates_from_str\nfrom time import time\n<\/pre>\n
    Import data<\/strong><\/p>\n
    # some example data\nmdata = sm.datasets.macrodata.load_pandas().data\n\n# prepare the dates index\ndates = mdata[['year', 'quarter']].astype(int).astype(str)\n\nquarterly = dates[\"year\"] + \"Q\" + dates[\"quarter\"]\n\nquarterly = dates_from_str(quarterly)\n\nmdata = mdata[['realgovt', 'tbilrate', 'cpi', 'realgdp']]\n\nmdata.index = pd.DatetimeIndex(quarterly)\n\ndf = np.log(mdata).diff().dropna()\n\ndisplay(df)\n<\/pre>\n
    \n
    \n