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 57.20% per annum.
- CRM price at the close of March 27, 2025 was $277.81 and was lower than the bottom border of the primary price channel by $97.27 (25.93%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 29.58% per annum.
- CRM price at the close of March 27, 2025 was inside the secondary price channel.
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 CRM 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: August 26, 2022
End date: May 24, 2024
a = 3.8347
b = 0.0012
s = 0.0835
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 57.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0835) – 1
= 39.64%
August 26, 2022 calculations
Top border of price channel:
Exp(Y608)
= Exp(a + b × X608 + 2 × s)
= Exp(a + b × 879 + 2 × s)
= Exp(3.8347 + 0.0012 × 879 + 2 × 0.0835)
= Exp(5.0911)
= $162.57
Bottom border of price channel:
Exp(Y608)
= Exp(a + b × X608 – 2 × s)
= Exp(a + b × 879 – 2 × s)
= Exp(3.8347 + 0.0012 × 879 – 2 × 0.0835)
= Exp(4.7572)
= $116.42
May 24, 2024 calculations
Top border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 + 2 × s)
= Exp(a + b × 1,516 + 2 × s)
= Exp(3.8347 + 0.0012 × 1,516 + 2 × 0.0835)
= Exp(5.8806)
= $358.01
Bottom border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 – 2 × s)
= Exp(a + b × 1,516 – 2 × s)
= Exp(3.8347 + 0.0012 × 1,516 – 2 × 0.0835)
= Exp(5.5467)
= $256.38
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 57.20% per annum.
- CRM price at the close of March 27, 2025 was $277.81 and was lower than the bottom border of the primary price channel by $97.27 (25.93%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 2, 2023
End date: March 27, 2025
a = 4.5064
b = 0.0007
s = 0.0952
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.58%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0952) – 1
= 46.37%
March 2, 2023 calculations
Top border of price channel:
Exp(Y736)
= Exp(a + b × X736 + 2 × s)
= Exp(a + b × 1,067 + 2 × s)
= Exp(4.5064 + 0.0007 × 1,067 + 2 × 0.0952)
= Exp(5.4544)
= $233.79
Bottom border of price channel:
Exp(Y736)
= Exp(a + b × X736 – 2 × s)
= Exp(a + b × 1,067 – 2 × s)
= Exp(4.5064 + 0.0007 × 1,067 – 2 × 0.0952)
= Exp(5.0735)
= $159.73
March 27, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.5064 + 0.0007 × 1,823 + 2 × 0.0952)
= Exp(5.9912)
= $399.88
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.5064 + 0.0007 × 1,823 – 2 × 0.0952)
= Exp(5.6102)
= $273.20
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 29.58% per annum.
- CRM price at the close of March 27, 2025 was inside the secondary price channel.
- 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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