As the incidence of the structural break is a binary outcome (1 if the structural break occurred and 0 otherwise) we model it in the logistic regression type of environment. We use variety of models from the logistic regression family. We start off with Logit and Probit, and then further extend our analysis by introducing ordered versions of the model when we jointly model probability of no structural break (denoted 1), structural break when the trend mean will correct downward (denoted 0), and structural break when the trend mean will correct upward (denoted 2). Furthermore, in addition to traditional econometric and statistical techniques, we also use machine learning technique known as extreme gradient boosting to further improve our models.

The set of determinants include many determinants that vary greatly from time series to time series. (It should be also noted that in some moedl version of XGBoost we let the model pick optimal set of variables from all variables with same (or higher) frequency as the variable of interest). Overall, the determinants can be broadly categorized into the following groups:

1. ARIMA and GARCH type of autoregressive components (e.g. the change in the price)
2. Seasonal dummies (e.g., minute of the hour, hour of day, day of week, etc) depending on frequency of data analyzed
3. Macroeconomic soundness indicators (e.g., infl ation, unemployment, etc.)
4. Macroeconomic crisis dummy (banking, debt, or currency crisis)
5. Substitutes and complements prices and quantities
6. Prices and quantities of other goods in the supply chain
7. Stock market measures and ratios based on price, volume, and capitalization
8. Order books (e.g. movement in the unrealized part of orders on the exchange)
9. Online/social media activity that can be subdivided into: NLP crawls of relevant news outlets, sentiment analysis of social media postings, count of searches on google, etc.
10. Unrelated but deterministic variables (Z)

For each variable we include own determinants from the list, but also determinants of all other time series. W hile this approach is computationally intensive and statistically incorrect, there is a consensus in the literature that overspecified provide more accurate forecast and have been broadly used (e.g. FED, etc.). Therefore, we follow the literature and, in cases where they perform better, we adapt the models that include all available variables. If we consider Bitcoin price the important determinants of structural break are recent price movements, Bitcoin market parameters like one-period change in order books, volatility of volume in recent past, sudden changes in volume, persistent one-directional pressure on price, etc. There are also market measures that are not related to Bitcoin. For example, changes in the USD Tether market capitalization also play crucial importance in predicting the probability of structural break. Furthermore, the ratio of Bitcoin and Ethereum volume to volume of all cryptocurrencies pegged to fiat currencies (i.e., “stable coins”) is also important determinant of probability of a structural break in Bitcoin price.

To predict structural breaks in 12,000 time series we use nearly million variables with use data from nearly 300 sources.

Some of the sources include: American Financial Exchange, Andrew Davidson & Co., Inc., Automatic Data Processing, Inc., Bank for International Settlements, Bank of England, Bank of Italy, Bank of Japan, Bank of Mexico, Binance, Bittsanalytics, Board of Governors of the Federal Reserve System (US), Cass Information Systems, Inc., Center for Financial Stability, Centers for Disease Control and Prevention, Central Bank of the Republic of Turkey, Chicago Board Options Exchange, Coinbase, Conference of State Bank Supervisors, Council of Economic Advisers (US), CredAbility Nonprofit Credit Counseling & Education, Dartmouth Atlas of Healthcare, Deutsche Bundesbank, DHI Group, Inc., Dow Jones & Company, Economic Freedom Network, Economist Intelligence Unit, Equifax, European Central Bank, Eurostat, Federal Bureau of Investigation, Federal Deposit Insurance Corporation, Federal Financial Institutions Examination Council (US), Federal Reserve Bank of Atlanta, Federal Reserve Bank of Chicago, Federal Reserve Bank of Cleveland, Federal Reserve Bank of Dallas, Federal Reserve Bank of Kansas City, Federal Reserve Bank of New York, Federal Reserve Bank of Philadelphia, Federal Reserve Bank of Richmond, Federal Reserve Bank of San Francisco, Federal Reserve Bank of St. Louis, Freddie Mac, UK Office for National Statistics, Haver Analytics, Ice Data Indices, LLC, Indeed, Indiana University: Indiana Business Research Center, International Monetary Fund, Moody’s, NASDAQ OMX Group, National Association of Realtors, National Bureau of Economic Research, Nikkei Industry Research Institute, Oklahoma State University, Optimal Blue, Organization for Economic Co-operation and Development, Realtor.com, Reserve Bank of Australia, S&P Dow Jones Indices LLC, Swiss National Bank, United Nations, University of Pennsylvania, U.S. Bureau of Economic Analysis, U.S. Bureau of Labor Statistics, U.S. Bureau of Transportation Statistics, U.S. Census Bureau, U.S. Congressional Budget Office, U.S. Department of Housing and Urban Development, U.S. Department of Labor, U.S. Department of the Treasury, U.S. Department of the Treasury. Fiscal Servicem, U.S. Department of the Treasury. Internal Revenue Service, U.S. Employment and Training Administration, U.S. Energy Information Administration, U.S. Federal Highway Administration, U.S. Federal Housing Finance Agency, U.S. Federal Open Market Committee, U.S. Office of Management and Budget, U.S. Patent and Trademark Office, World Bank, and Zillow.