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 5.29% per annum.
- DIS price at the close of April 25, 2025 was $90.28 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 74.16% per annum.
- DIS price at the close of April 25, 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 DIS 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: September 22, 2022
End date: April 2, 2025
a = 4.3829
b = 0.0001
s = 0.0946
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.29%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0946) – 1
= 46.00%
September 22, 2022 calculations
Top border of price channel:
Exp(Y607)
= Exp(a + b × X607 + 2 × s)
= Exp(a + b × 878 + 2 × s)
= Exp(4.3829 + 0.0001 × 878 + 2 × 0.0946)
= Exp(4.6961)
= $109.52
Bottom border of price channel:
Exp(Y607)
= Exp(a + b × X607 – 2 × s)
= Exp(a + b × 878 – 2 × s)
= Exp(4.3829 + 0.0001 × 878 – 2 × 0.0946)
= Exp(4.3176)
= $75.01
April 2, 2025 calculations
Top border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 + 2 × s)
= Exp(a + b × 1,801 + 2 × s)
= Exp(4.3829 + 0.0001 × 1,801 + 2 × 0.0946)
= Exp(4.8265)
= $124.77
Bottom border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 – 2 × s)
= Exp(a + b × 1,801 – 2 × s)
= Exp(4.3829 + 0.0001 × 1,801 – 2 × 0.0946)
= Exp(4.4480)
= $85.46
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.29% per annum.
- DIS price at the close of April 25, 2025 was $90.28 and was inside the primary price channel.
Secondary Trend
Start date: January 27, 2025
End date: April 25, 2025
a = 11.2105
b = -0.0037
s = 0.0446
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0037) – 1
= -74.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0446) – 1
= 19.55%
January 27, 2025 calculations
Top border of price channel:
Exp(Y1,194)
= Exp(a + b × X1,194 + 2 × s)
= Exp(a + b × 1,736 + 2 × s)
= Exp(11.2105 + -0.0037 × 1,736 + 2 × 0.0446)
= Exp(4.8633)
= $129.44
Bottom border of price channel:
Exp(Y1,194)
= Exp(a + b × X1,194 – 2 × s)
= Exp(a + b × 1,736 – 2 × s)
= Exp(11.2105 + -0.0037 × 1,736 – 2 × 0.0446)
= Exp(4.6847)
= $108.28
April 25, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(11.2105 + -0.0037 × 1,824 + 2 × 0.0446)
= Exp(4.5370)
= $93.41
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(11.2105 + -0.0037 × 1,824 – 2 × 0.0446)
= Exp(4.3584)
= $78.13
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 74.16% per annum.
- DIS price at the close of April 25, 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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