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 7.08% per annum.
- TSLA price at the close of January 17, 2025 was $426.50 and was higher than the top border of the primary price channel by $125.74 (41.81%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 209.14% per annum.
- TSLA price at the close of January 17, 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 TSLA 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: December 4, 2020
End date: October 23, 2024
a = 5.6492
b = -0.0002
s = 0.2120
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.2120) – 1
= 133.52%
December 4, 2020 calculations
Top border of price channel:
Exp(Y222)
= Exp(a + b × X222 + 2 × s)
= Exp(a + b × 318 + 2 × s)
= Exp(5.6492 + -0.0002 × 318 + 2 × 0.2120)
= Exp(6.0092)
= $407.18
Bottom border of price channel:
Exp(Y222)
= Exp(a + b × X222 – 2 × s)
= Exp(a + b × 318 – 2 × s)
= Exp(5.6492 + -0.0002 × 318 – 2 × 0.2120)
= Exp(5.1611)
= $174.36
October 23, 2024 calculations
Top border of price channel:
Exp(Y1,198)
= Exp(a + b × X1,198 + 2 × s)
= Exp(a + b × 1,737 + 2 × s)
= Exp(5.6492 + -0.0002 × 1,737 + 2 × 0.2120)
= Exp(5.7236)
= $306.01
Bottom border of price channel:
Exp(Y1,198)
= Exp(a + b × X1,198 – 2 × s)
= Exp(a + b × 1,737 – 2 × s)
= Exp(5.6492 + -0.0002 × 1,737 – 2 × 0.2120)
= Exp(4.8755)
= $131.04
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.08% per annum.
- TSLA price at the close of January 17, 2025 was $426.50 and was higher than the top border of the primary price channel by $125.74 (41.81%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 13, 2024
End date: January 17, 2025
a = 0.3012
b = 0.0031
s = 0.1296
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0031) – 1
= 209.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1296) – 1
= 67.96%
March 13, 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(0.3012 + 0.0031 × 1,513 + 2 × 0.1296)
= Exp(5.2389)
= $188.47
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,513 – 2 × s)
= Exp(0.3012 + 0.0031 × 1,513 – 2 × 0.1296)
= Exp(4.7204)
= $112.21
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(0.3012 + 0.0031 × 1,823 + 2 × 0.1296)
= Exp(6.1975)
= $491.53
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(0.3012 + 0.0031 × 1,823 – 2 × 0.1296)
= Exp(5.6790)
= $292.65
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 209.14% per annum.
- TSLA price at the close of January 17, 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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