Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 52.15% per annum.
- CTAS price at the close of January 8, 2025 was $192.28 and was lower than the bottom border of the primary price channel by $17.11 (8.17%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 88.06% per annum.
- CTAS price at the close of January 8, 2025 was higher than the top border of the secondary price channel by $3.85 (2.04%). This indicates a possible reversal in the secondary trend direction.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of CTAS price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: February 21, 2023
End date: December 17, 2024
a = 3.3134
b = 0.0011
s = 0.0345
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 52.15%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0345) – 1
= 14.78%
February 21, 2023 calculations
Top border of price channel:
Exp(Y784)
= Exp(a + b × X784 + 2 × s)
= Exp(a + b × 1,139 + 2 × s)
= Exp(3.3134 + 0.0011 × 1,139 + 2 × 0.0345)
= Exp(4.6920)
= $109.08
Bottom border of price channel:
Exp(Y784)
= Exp(a + b × X784 – 2 × s)
= Exp(a + b × 1,139 – 2 × s)
= Exp(3.3134 + 0.0011 × 1,139 – 2 × 0.0345)
= Exp(4.5542)
= $95.03
December 17, 2024 calculations
Top border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 + 2 × s)
= Exp(a + b × 1,804 + 2 × s)
= Exp(3.3134 + 0.0011 × 1,804 + 2 × 0.0345)
= Exp(5.4567)
= $234.33
Bottom border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 – 2 × s)
= Exp(a + b × 1,804 – 2 × s)
= Exp(3.3134 + 0.0011 × 1,804 – 2 × 0.0345)
= Exp(5.3189)
= $204.16
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 52.15% per annum.
- CTAS price at the close of January 8, 2025 was $192.28 and was lower than the bottom border of the primary price channel by $17.11 (8.17%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 21, 2024
End date: January 6, 2025
a = 15.8031
b = -0.0058
s = 0.0337
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0058) – 1
= -88.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0337) – 1
= 14.43%
November 21, 2024 calculations
Top border of price channel:
Exp(Y1,226)
= Exp(a + b × X1,226 + 2 × s)
= Exp(a + b × 1,778 + 2 × s)
= Exp(15.8031 + -0.0058 × 1,778 + 2 × 0.0337)
= Exp(5.5182)
= $249.19
Bottom border of price channel:
Exp(Y1,226)
= Exp(a + b × X1,226 – 2 × s)
= Exp(a + b × 1,778 – 2 × s)
= Exp(15.8031 + -0.0058 × 1,778 – 2 × 0.0337)
= Exp(5.3834)
= $217.77
January 6, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(15.8031 + -0.0058 × 1,824 + 2 × 0.0337)
= Exp(5.2504)
= $190.64
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(15.8031 + -0.0058 × 1,824 – 2 × 0.0337)
= Exp(5.1156)
= $166.60
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 88.06% per annum.
- CTAS price at the close of January 8, 2025 was higher than the top border of the secondary price channel by $3.85 (2.04%). This indicates a possible reversal in the secondary trend direction.
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