Articles from:August 2024

  • Samiha Tasnim Masters Project Presentation Monday, August 19, 10:30 AM

    Samiha Tasnim, a Master of Science candidate in the Department of Mathematics and Statistics, will present their Masters Research Project (STAT 5P99) titled The Impact of Exchange Rate Data on Canadian Inflation: An FPCA and Group LASSO Approach on Monday, August 19, 2024 at 10:30 AM online on Microsoft Teams.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. If you are interested in the presentation, please contact Neil Marshall at [email protected] for a link to the Team.

    Abstract: This study investigates the temporal dynamics of exchange rates between various international currencies and the Canadian dollar, with a focus on understanding how these rates influence Canadian inflation. The Functional Principal Component Analysis (FPCA) is applied to effectively reduce the dimensionality of exchange rate data and capture important modes of variation. The extracted functional principal components (FPCs) were then used in a Group LASSO regression model to identify which currencies most significantly impact inflation rates in Canada. Our analysis includes exchange rates from nine countries. The results show that the U.S. Dollar (USD), Mexican Peso (MXN), and Swedish Krona (SEK) are the most influential currencies in predicting Canadian inflation rates. By employing these advanced statistical techniques, this study provides a comprehensive assessment of how fluctuations in global currencies can affect the domestic economic environment, offering valuable insights for policymakers and financial analysts. This study contributes to the broader understanding of currency exchange impacts on inflation and highlights the importance of specific international currencies in economic forecasting.

    Keywords: Functional Principal Component Analysis, Group LASSO, inflation rate, exchange rates, economic indicators, predictive modeling, advanced statistical techniques

  • Department of Mathematics and Statistics Colloquium Talk: Dr. Basil Nanayakkara

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Basil Nanayakkara on Thursday, August 22nd, 2024 from 2:00 PM to 3:00 PM. The talk is entitled Quaternion algebras and the Frobenius theorem – Part 2.

    For location room number, please email Neil Marshall ([email protected]).

    Abstract:
    (This is a continuation of the seminar on July 25th. However, you will be able to understand this, even if you didn’t attend Part 1, as we will be discussing mainly the Frobenius theorem).

    Given a field k and nonzero elements a, b in k, we’ll construct a quaternion algebra over k associated with a and b. We’ll show that it is a central simple algebra, and hence determines an element in the Brauer group of k. Moreover, we’ll see that this quaternion algebra is a division algebra iff the norm function admits a nontrivial zero.

    A related result is the Frobenius theorem, which states that the finite dimensional division algebras over R are R, C and H only, thereby proving that the Brauer group of R is the cyclic group of order 2.

    The geometric counterpart of a quaternion algebra is a one-dimensional Brauer-Severi variety. If time permits, we’ll discuss this notion as well.