Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 36.77% per annum.
- MRK price at the close of March 3, 2025 was $93.15 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1,051.79% per annum.
- MRK price at the close of March 3, 2025 was inside the secondary price channel.
- 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 MRK 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: April 25, 2024
End date: March 3, 2025
a = 6.7913
b = -0.0013
s = 0.0355
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -36.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0355) – 1
= 15.26%
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 + 2 × s)
= Exp(a + b × 1,513 + 2 × s)
= Exp(6.7913 + -0.0013 × 1,513 + 2 × 0.0355)
= Exp(4.9625)
= $142.95
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,513 – 2 × s)
= Exp(6.7913 + -0.0013 × 1,513 – 2 × 0.0355)
= Exp(4.8205)
= $124.03
March 3, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(6.7913 + -0.0013 × 1,825 + 2 × 0.0355)
= Exp(4.5707)
= $96.61
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.7913 + -0.0013 × 1,825 – 2 × 0.0355)
= Exp(4.4287)
= $83.82
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 36.77% per annum.
- MRK price at the close of March 3, 2025 was $93.15 and was inside the primary price channel.
Secondary Trend
Start date: February 13, 2025
End date: March 3, 2025
a = -7.6785
b = 0.0067
s = 0.0168
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0067) – 1
= 1,051.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0168) – 1
= 6.94%
February 13, 2025 calculations
Top border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 + 2 × s)
= Exp(a + b × 1,807 + 2 × s)
= Exp(-7.6785 + 0.0067 × 1,807 + 2 × 0.0168)
= Exp(4.4540)
= $85.97
Bottom border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 – 2 × s)
= Exp(a + b × 1,807 – 2 × s)
= Exp(-7.6785 + 0.0067 × 1,807 – 2 × 0.0168)
= Exp(4.3869)
= $80.39
March 3, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(-7.6785 + 0.0067 × 1,825 + 2 × 0.0168)
= Exp(4.5745)
= $96.98
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(-7.6785 + 0.0067 × 1,825 – 2 × 0.0168)
= Exp(4.5074)
= $90.69
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1,051.79% per annum.
- MRK price at the close of March 3, 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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