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 51.40% per annum.
- CTAS price at the close of January 16, 2025 was $198.05 and was lower than the bottom border of the primary price channel by $12.44 (5.91%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 71.51% per annum.
- CTAS price at the close of January 16, 2025 was higher than the top border of the secondary price channel by $0.33 (0.16%). 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 6, 2023
End date: December 17, 2024
a = 3.3459
b = 0.0011
s = 0.0357
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 51.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0357) – 1
= 15.33%
February 6, 2023 calculations
Top border of price channel:
Exp(Y768)
= Exp(a + b × X768 + 2 × s)
= Exp(a + b × 1,116 + 2 × s)
= Exp(3.3459 + 0.0011 × 1,116 + 2 × 0.0357)
= Exp(4.6853)
= $108.35
Bottom border of price channel:
Exp(Y768)
= Exp(a + b × X768 – 2 × s)
= Exp(a + b × 1,116 – 2 × s)
= Exp(3.3459 + 0.0011 × 1,116 – 2 × 0.0357)
= Exp(4.5427)
= $93.94
December 17, 2024 calculations
Top border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 + 2 × s)
= Exp(a + b × 1,796 + 2 × s)
= Exp(3.3459 + 0.0011 × 1,796 + 2 × 0.0357)
= Exp(5.4580)
= $234.63
Bottom border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 – 2 × s)
= Exp(a + b × 1,796 – 2 × s)
= Exp(3.3459 + 0.0011 × 1,796 – 2 × 0.0357)
= Exp(5.3154)
= $203.44
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 51.40% per annum.
- CTAS price at the close of January 16, 2025 was $198.05 and was lower than the bottom border of the primary price channel by $12.44 (5.91%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 7, 2024
End date: January 14, 2025
a = 11.4835
b = -0.0034
s = 0.0421
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0034) – 1
= -71.51%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0421) – 1
= 18.32%
November 7, 2024 calculations
Top border of price channel:
Exp(Y1,210)
= Exp(a + b × X1,210 + 2 × s)
= Exp(a + b × 1,756 + 2 × s)
= Exp(11.4835 + -0.0034 × 1,756 + 2 × 0.0421)
= Exp(5.5276)
= $251.55
Bottom border of price channel:
Exp(Y1,210)
= Exp(a + b × X1,210 – 2 × s)
= Exp(a + b × 1,756 – 2 × s)
= Exp(11.4835 + -0.0034 × 1,756 – 2 × 0.0421)
= Exp(5.3594)
= $212.60
January 14, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(11.4835 + -0.0034 × 1,824 + 2 × 0.0421)
= Exp(5.2938)
= $199.09
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(11.4835 + -0.0034 × 1,824 – 2 × 0.0421)
= Exp(5.1255)
= $168.26
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 71.51% per annum.
- CTAS price at the close of January 16, 2025 was higher than the top border of the secondary price channel by $0.33 (0.16%). This indicates a possible reversal in the secondary trend direction.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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