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    "# Introduction to Morden Time Series Forecasting\n",
    "\n",
    "## Feng Li\n",
    "\n",
    "### Guanghua School of Management\n",
    "### Peking University\n",
    "\n",
    "\n",
    "### [feng.li@gsm.pku.edu.cn](feng.li@gsm.pku.edu.cn)\n",
    "### Course home page: [https://feng.li/bdcf](https://feng.li/bdcf)"
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    "## Elements of good forecasts: *state-of-the-art perspectives*\n",
    "\n",
    "-   Robust again a large collection of time series data.\n",
    "\n",
    "    -   What if I do not have any benchmark data?\n",
    "    -   Build a model on machine-generated data and test on real data.\n",
    "\n",
    "-   Properly tackling model uncertainty and data uncertainty.\n",
    "\n",
    "    -   What shall we do when all forecasting models fail?\n",
    "    -   Can we forecast without historical data?\n",
    "\n",
    "-   Good speed performance with a large scale of time series.\n",
    "\n",
    "    -   Most forecast models could not scale up.\n",
    "    -   A need for a distributed forecasting framework."
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    "## Time series features\n",
    "\n",
    "- Features of time series produce more accurate forecasting accuracies.\n",
    "\n",
    "- Features give forecasting method selection rules.\n",
    "\n",
    "- \"Horses for courses\": effects of time series features for the forecasting performances.\n",
    "\n",
    "-  Visualize the performances of different forecasting methods in a 2D space for a better understanding of their relative performances."
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    "![image.png](figures/time-series-features.png)"
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    "## Predict the forecasting model performance\n",
    "\n",
    "-   Train a time series model (*machine learning with dependent data*)\n",
    "    is usually costly.\n",
    "\n",
    "-   New algorithms a re developed every day.\n",
    "\n",
    "-   A well trained model with `my dataset` does not necessary work well\n",
    "    for `your dataset`. Why?\n",
    "\n",
    "-   Is there a way to **forecast which algorithm works the best** for\n",
    "    any time series *ex-ante* ?\n",
    "\n",
    "    -   Unrealistic because we could not collect all the time series in\n",
    "        the world.\n",
    "    -   But we could work on the time series feature space."
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    "## Distributed forecasting with ultra-long time series\n",
    "\n",
    "-   Ultra-long time series are increasingly accumulated in many cases.\n",
    "\n",
    "    -   hourly electricity demands\n",
    "\n",
    "    -   daily maximum temperatures\n",
    "\n",
    "    -   streaming data generated in real-time\n",
    "\n",
    "-   Forecasting these time series is challenging.\n",
    "\n",
    "    -   time-consuming training process\n",
    "\n",
    "    -   hardware requirements\n",
    "\n",
    "    -   unrealistic assumption that the DGP remains invariant over a\n",
    "        long time interval"
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    "![electricity-example.png](figures/electricity-example.png)\n",
    "\n",
    "https://doi.org/10.1016/j.ijforecast.2022.05.001"
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    "## Hierarchical time series\n",
    "\n",
    "-   Hierarchical time series are special network data.\n",
    "\n",
    "-   Constants exist that the forecasts on each hierarchy should be **coherent** with the aggregation structure.\n"
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   "source": [
    "![image](figures/M5data.png)\n",
    "https://doi.org/10.1016/j.ijforecast.2021.12.015"
   ]
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    "## Hierarchical forecasting\n",
    "\n",
    "-   Hard to use multivariate time series models, like VARs, because the bottom level is highly noisy or intermittent.\n",
    "\n",
    "-   Copula models are hard to scale up.\n",
    "\n",
    "-   Pure deep learning models fail to meet the **coherent constant**."
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